00:02
This is five dimensions.
00:07
This is from a point to a line in five dimensions.
00:11
Okay, so we have our line in parametric form, negative three, negative two t, one plus two t, negative t, negative t, negative t, two plus two, 5t.
00:39
Okay, and then we have our point p.
00:45
1, 2, 3, 2, 1.
00:55
Okay, i want to make sure i didn't write that down incorrectly.
00:59
Negative 3, negative 2t, 1 plus 2t, negative t, 2 plus 5t.
01:06
Okay, our point q, that is on the line.
01:09
I'm just going to let t equal 0, negative 3, 0.
01:18
1, 0, 2, r vector v, which is in the direction of the line.
01:38
I just need to take the coefficients of t.
01:40
So there's 0 t in the first one, negative 2t in the second one, 2t in the third one, negative 1t in the fourth one, and the fifth one has 5t.
02:03
Okay, vector w.
02:08
Which will extend from q to p.
02:12
So i just need to take p minus q.
02:14
1 minus negative 3 is 1 plus 3, which is 4.
02:21
2 minus 0 is 2.
02:24
3 minus 1 is 2.
02:26
2 minus 0 is 2.
02:29
1 minus 2 is negative 1.
02:33
Now we can just use our formula, although you can think about it too, the projection of vector w in the direction of vector v.
02:48
The inner product of w and v over the inner product of v and v and the direction v.
02:57
The inner product of w and v and v.
03:01
W, yeah, w and v is zero minus four plus four, minus two.
03:19
And then that's also going to be minus five.
03:24
I'm just making sure i didn't make a mistake.
03:28
Negative four, positive four, negative two, negative five.
03:32
Okay.
03:34
And interproduct of v and v.
03:38
4 plus 4 plus 1 plus 5.
03:45
No.
03:46
4 plus 4 plus 1 plus 25.
03:50
5 times 5 is 25.
03:56
Okay.
03:57
And then we need to multiply.
03:57
That by 0, negative 2, 2, negative 1.
04:06
Okay, negative 2 minus 5 is negative 7, 26, 34.
04:23
Okay, 0, negative 2, come on, negative 1, 5.
04:37
That's going to give us 0, 34, 7, 7, 34, 3, 4, 3 ,000, 2, come on, negative 1, 5.
04:46
By 2 is 17, negative 7, 17ths, 7 34ths, and negative 35, 34ths.
05:12
Now, we need to do the vector w minus the projection.
05:34
So scroll up a little so i can see it.
05:38
I can't do that.
05:42
Okay, 4 minus 0 is 4.
05:46
2 minus 7 .17th.
05:51
That's 34 minus 7.
05:55
That would be 2717s.
06:10
Because 2 is 3417th, minus 717th, 27th.
06:19
Okay.
06:27
Now we need to, plus 717s.
06:33
So that's 34 plus 7 .41 17th.
06:43
Now we need negative 1...