00:01
Okay, so here's the information that we're given.
00:02
We're given a u vector, which is 3, negative 1, 4.
00:05
And we're given a v vector, which is negative 2, 2, 1.
00:08
And we want to find the angle between them and the area of the triangle made by those two.
00:14
So, if we start with the angle, you have to do the dot product of the two, which is just a dot b.
00:25
But there's another way of writing that.
00:27
It's the magnitude of a dot b equals the magnitude of a times the magnitude of b cosine theta.
00:38
That's the formula that we need to use right there.
00:44
So, if we were to find the magnitude, we'd do 3 times negative 2 plus negative 1 times 2 plus 4 times 1.
00:56
This equals negative 6 minus 2 plus 4, which equals negative 4.
01:07
All right, that's the magnitude of a dot b.
01:13
So, then the magnitude of a equals, that's when you do 3 squared plus negative 1 squared plus 4 squared.
01:28
And you take the square root of all that.
01:30
That equals the square root of 26...