Answer
u∙u = 5
v∙u = 8
(v∙u) / (u∙u) = 8/5 = 1.6
Work Step by Step
Note: The vectors can be rewritten as with <>, so
u =
v=<4,6>
Part A: u∙u
This asks for the dot product of u and u.
The dot product can be determined by multiplying the first component of the vectors together, multiplying the second component of the vectors together, and adding those products together.
1. Multiply the first components: -1 * -1 = 1
2. Multiply the second components: 2 * 2 = 4
3. Add the two products together: 1 + 4 = 5
The dot product is 5.
Part B: v∙u
This asks for the dot product of v and u.
The dot product can be determined by multiplying the first component of the vectors together, multiplying the second component of the vectors together, and adding those products together.
1. Multiply the first components: 4*-1 = -4
2. Multiply the second components: 6 * 2 = 12
3. Add the two products together: -4 + 12 = 8
The dot product is 8.
Part C: (v∙u) / (u∙u)
This asks for the dot product of v and u to be divided by the dot product of u and u. Since the dot products were previously solved for, we can just divide the two dot products.
1. Divide the two dot products: 8 / 5 = 1.6
The answer is 1.6
