00:01
For this question, we're given four points, a, b, c, d, and we're shown vectors one and vectors two, vector one, vector two.
00:09
And we're asked to write each the vectors or the sum of the vectors as a product, or as the sum of components of v1, v2.
00:20
So the first one we want to find is the vector c -a.
00:28
Okay.
00:29
And so what we're going to do is we're just going to count, right? we're going to count in the v1 direction and then the v2 direction.
00:39
And what i'm going to do is i'm going to write these in the component form first like this, and then we'll write them as a sum.
00:45
So you can see here we're going to go one, two, three, four, five, six, six v -1s.
00:54
And then we're going to go one, two, three, four, five, six v2.
01:00
So six, six.
01:02
Let me get rid of those.
01:03
Or else it's going to get too crowded.
01:06
So 6, 6, which of course would be 6 e sub 1 plus 6 piece of 2.
01:17
All right.
01:18
So that is the first one they asked for.
01:21
The second one they asked for is vector b .a.
01:28
Minus vector d .a.
01:33
And again, i'm going to write the component parts for each.
01:36
I'll do the subtraction and then i'll change it to its final form.
01:39
So b -a, i'm going to see that i have 1, 2, 3, 4, and 1.
01:48
So the component form is going to be 4 -1, and i'm going to subtract.
01:58
And then da, now if i try to go the v1 direction first, i'm going to go off the graph.
02:02
So i'm going to go this in the reverse order.
02:05
So 1, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3.
02:13
So i counted in the v2 direction first and then the v1 direction.
02:18
So that was 9 and 3.
02:19
So my component form is going to be 3 .9.
02:25
So when i do this subtraction, i'm going to get 4 minus 3 is 1...