00:01
So we have two vectors, u and v, but v is missing a component and it's called y.
00:06
We're trying to find y, so the angle between them is 60 degrees.
00:11
And we have this formula here that we're going to use.
00:14
So let's start working.
00:16
Cosine theta.
00:18
Theta is supposed to be 60.
00:21
U dotted with v, so that's 1 times 4 plus 5 times y.
00:29
And the bottom is magnitude of u so that's one squared plus five squared and a magnitude of v is four squared plus y squared okay let's simplify further this is going to say cosine 60 equals four plus five y one squared is 1, 5 squared is 25, so that's radical 26, and then this is 16 plus y squared.
01:12
Cosine 60 can be found in your calculator.
01:15
You get one half, and that's 4 plus 5 y over, and i can combine them, 26 times 16 plus y squared.
01:34
And then it's basically a proportion, and you can do the cross products.
01:38
You can do the one times that and the two times that.
01:42
So the cross, the diagonals are going to be equal.
01:45
So really, it's radical 26 times 16 plus y squared, and that's going to equal two times four plus five y.
01:59
We have this mess of an equation to solve.
02:02
I basically did the cross products.
02:04
That times that equals that times that.
02:08
So let's keep simplifying.
02:11
Actually, although up here.
02:14
So that on the left -hand side, 26 times 16 gives us 416 plus 26 y squared.
02:31
If i distribute that and that.
02:34
And then that equals, and i've got to distribute here and here as well.
02:39
So 2 times 4 is 8 plus 2 times 5 y is 10.
02:45
And now we have this lovely equation.
02:49
This square root needs to go away.
02:51
So let's square both sides.
02:56
So that's going to be 416, my plus 26 y squared.
03:03
You have to do 8 plus 10 y times 8 plus 10 y and then use foil...