00:01
In this question, we are asked to find the angle between the given vectors.
00:05
Let's give names to the vectors.
00:08
Let's call the first vector u1 and the second vector u2.
00:15
Then the dot product of u1 and u2 equals to the length of u1, multiplied by the length of u2, multiplied by cos theta, where, sorry, cos alpha, where alpha is the angle between the vectors that we are trying, to find in this question.
00:36
From that equation, cost alpha equals to u1 .u2 divided by the length of u1, multiplied by the length of u2.
00:49
And now we need to calculate the length of each vector and there can calculate their dot product.
00:57
To find the dot product, we need to multiply the coordinates of vectors and then add them up.
01:10
We are going to get negative 5 times negative 2, which is the product of the x chord, plus 3 times 6 which is the product of the y coordinates.
01:26
This equals to 10 plus 18 equals to 28.
01:32
This is a dot product.
01:37
Now we need to calculate the length of each vector.
01:42
And to do that we need to calculate the square root of the sum of the squares of coordinates.
01:49
For example, to find the length of u1, we need to square each coordinate we are going to get negative 5 squared plus 3 squared square the coordinates add them up and take the square root this simplifies to the square root of 25 plus 9 and the square root of 25 plus 9 equals to the square root of 34 sorry that's the length of you 1 the length of u 2 equals to the square root of 0 of 9 negative 2 squared plus 6 squared.
02:34
That's going to be the square root of 4 plus 36 and this equals to the square root of 40.
02:47
Therefore, cos alpha equals to 28 divided by the square root of 34 times the square root of 40...