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126
help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:46:11
well
1
0
null
null
null
null
null
126
help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:46:26
Let's take T1
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1
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:46:31
okay
1
0
null
null
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null
null
126
help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:46:39
<5, -5, 5>
1
0
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null
126
help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:46:52
so that's 5 < 1, -1, 1>
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:47:00
and that vector left over is the unit vector?
1
0
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126
help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:48:06
Not exactly what I was trying to get you to do
0
1
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:48:12
ahh
1
0
null
null
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null
null
126
help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:48:44
Express each force in Cartesian vector form
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1
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:48:49
Do you know what that means?
0
1
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:48:56
using i j and k?
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:49:04
Yes
0
1
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:49:09
ah
1
0
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null
126
help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:49:13
5i - 5j + 5k
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:49:36
Not exactly, that's just the distance
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:49:46
uhhhh
1
0
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null
126
help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:49:55
I'm confused as to what you're asking 😅
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:50:10
You understand what the unit vector does, right?
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:50:24
It describes the direction as a unit length
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:50:55
It's a mag of 1, meaning if you took some other vector and multiplied it, it doesn't scale it
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:50:57
Right?
0
1
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:51:03
Yes
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:51:39
So we what to find the i, j, k form of each T1
0
1
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:51:53
I'll walk you through the first one
0
1
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a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:52:06
alright, sure
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:52:59
https://cdn.discordapp.c…688/IMG_0015.png
IMG_0015.png
1
0
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null
126
help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:53:03
Is this it?
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:53:17
Not exactly
0
1
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a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:53:25
that's a sqrt(75) in the denoms
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:53:27
aw rip
1
0
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null
126
help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:53:38
What is that which I did?
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:53:49
That's the unit vector
0
1
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126
help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:53:55
alright
1
0
null
null
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null
null
126
help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:54:01
If you multiply it by T1
0
1
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:54:16
Then that's the overall force vector
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:54:20
nice
1
0
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null
126
help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:54:48
So T1 time that unit vector, is what you need
0
1
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:55:08
Do the same process for all of the other tensions
0
1
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:55:33
so that calculation I did, that's correct so far then
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:55:39
Yes
0
1
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126
help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:55:39
I just repeat it
1
0
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126
help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:55:41
alright
1
0
null
null
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null
null
126
help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:55:42
Yep
0
1
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:55:44
I have all the others then
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:56:13
It's just variations of this one
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:56:56
So for T1, it's $T1\left[\frac{5 \hat{i} - 5 \hat{j} + 5 \hat{k}}{\sqrt{75}}\right]$
0
1
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126
help-10
a00d0894dffd4f3a8a384da5966174e6
510,789,298,321,096,700
TeXit
01/17/2022 20:57:15
**dldh06**
https://cdn.discordapp.c…210272391178.png
485903210272391178.png
0
1
null
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null
null
null
126
help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:57:18
yes
1
0
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126
help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:57:43
So that's T1 in i, j, k form
0
1
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:57:58
Is this what normal vectors are?
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:58:02
Yes
0
1
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:58:07
I think
0
1
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:58:28
Okie
1
0
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null
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:58:41
anyways, we have our Force for the first tension
1
0
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a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:58:44
and also the other 3
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:59:11
when we sum these, they're equal to the force of gravity (since they need to cancel each other out)?
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:59:26
So, if you rewrite it, it's 0.577T1 i - 0.577T1 j + 0.577T1 k
0
1
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:59:30
Right?
0
1
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 20:59:39
that's..
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 20:59:58
I just expanded this
0
1
510,789,298,321,096,700
TeXit
0796
TeXit
true
126
help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:00:14
I'd prefer leaving it as $\frac{5}{\sqrt{75}}\hat{i}...$
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
510,789,298,321,096,700
TeXit
01/17/2022 21:00:17
**Jukelyn**
https://cdn.discordapp.c…701055565827.png
347216701055565827.png
0
1
null
null
null
null
null
126
help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 21:00:25
That works too
0
1
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:00:28
yesh
1
0
null
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null
null
null
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:01:01
in any case, we have these unit vectors which lets us construct a representation of the forces of tension
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 21:01:10
Yes
0
1
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null
126
help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 21:01:32
So, as stated, sum of forces equals 0
0
1
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:01:43
now we would add all 4 of them and that should be equal to the force of gravity?
1
0
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a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:01:52
or rather, I guess it depends on the POV
1
0
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a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 21:02:06
So T1 + T2 + T3 + T4 - 150(9.81) = 0
0
1
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a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:02:19
they sum to 0, but grav is neg so it's 0+ 150 (g) = tensions
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:02:21
yes
1
0
485,903,210,272,391,200
dldh06
2659
dldh06
false
126
help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:02:34
wouldn't this lead to a system of 4 equations though?
1
0
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a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 21:03:04
Sorta
0
1
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null
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:03:46
hmm
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 21:04:15
$T1\left[\frac{5}{\sqrt{75}}\hat{i} - \frac{5}{\sqrt{75}}\hat{j} + \frac{5}{\sqrt{75}}\hat{k}\right] + T2 ... - 150(9.81) k = 0$
0
1
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help-10
a00d0894dffd4f3a8a384da5966174e6
510,789,298,321,096,700
TeXit
01/17/2022 21:04:56
**dldh06**
https://cdn.discordapp.c…210272391178.png
485903210272391178.png
0
1
null
null
null
null
null
126
help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:04:58
why the k at the end?
1
0
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 21:05:14
Because that force is in the k direction
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a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:05:19
oh right,
1
0
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a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 21:05:21
The weight
0
1
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null
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:05:24
yes ofc
1
0
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null
126
help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:05:38
so, I'm trying to add them but it's getting extremely messy
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0
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a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 21:05:44
Now, system of equations for x, y, z directions
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1
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a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:05:58
is there some kind of fundamental thing I'm missing that can simplify this quite a bit?
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a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 21:06:40
Probably, something like the force is all the same since they all have the same unit vector
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a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:06:40
The more I'm working with vectors, the more I'm realizing that I kinda failed learning about them in-depth
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a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:06:47
I see
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0
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a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 21:07:09
But do you now understand how to do the rest?
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a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:07:32
Kinda, it's just going to be extremely long
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0
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help-10
a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 21:07:47
Just a bit
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1
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a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 21:08:52
$T1 \frac{5}{\sqrt{75}}\hat{i} + T2 \frac{5}{\sqrt{75}}\hat{i} - T3 \frac{5}{\sqrt{75}}\hat{i} - T4 \frac{5}{\sqrt{75}}\hat{i} = 0$
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a00d0894dffd4f3a8a384da5966174e6
510,789,298,321,096,700
TeXit
01/17/2022 21:08:54
**dldh06**
https://cdn.discordapp.c…210272391178.png
485903210272391178.png
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a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 21:09:03
That's the x direction
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1
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a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:09:08
yes
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0
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a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:09:15
I have this written down so far
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a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:09:26
https://cdn.discordapp.c…644/IMG_0016.png
IMG_0016.png
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0
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a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:10:33
I forgot to write the k hat
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a00d0894dffd4f3a8a384da5966174e6
485,903,210,272,391,200
dldh06
01/17/2022 21:10:41
You're going to have 3 equations, with 4 unknowns
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1
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help-10
a00d0894dffd4f3a8a384da5966174e6
347,216,701,055,565,800
Jukelyn
01/17/2022 21:10:41
or the RHS
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