00:01
So our goal is to find the angle between two vectors.
00:05
They have it written with i's and j's.
00:07
Those i's and j's, we're able to remove them and just represent it as vector u.
00:14
Vector u is, let's see, 2 and negative 1.
00:29
And then vector v is 10 and negative 5.
00:40
Whenever we need to find the angle between vectors, we're going to use the formula cosine theta is equal to the dot product, erase that, the dot product of vector u and vector v over the magnitude of vector u and the product of vector u and vector v.
01:15
So let's start off with the dot product.
01:17
The dot product, we're going to go ahead and multiply.
01:20
So we would have, let's see, dot product, let me write this out, is going to be 2 times 10 plus our y values, the product of our y's, which is negative 1 times negative 5.
01:43
2 times 10 is 20 plus negative 1 times negative 5 is 5.
01:50
So we would know that it is 25.
01:55
Our next step is to find the magnitude.
01:59
So we're going to start off with the magnitude of u.
02:05
The magnitude is equal to the square root of your x values plus your x squared and y squared.
02:11
So i'm going to have 2 squared plus negative 1 squared.
02:21
2 squared is 4, negative 1 squared is 1, so that would give me the square root of 5.
02:30
We're going to leave it in square root form.
02:32
We're not going to use decimals.
02:34
Our next step is the magnitude of v.
02:37
To find the magnitude of v, we're going to do the same thing as before.
02:41
It's going to be the square root of our x squared plus y squared.
02:45
So it would be 10 squared plus negative 5 squared.
02:53
10 squared is 100, negative 5 squared is 25...