Question

Suppose that u and v are vectors in R to the seventh power both of length 2 the square root of 2 and that the length of u − v is also2 the square root of 2 . Thenparallel-to u plus v parallel-to

Answer 1

The angle between u and v is π/3 and parallel-to u plus v parallel-to = k*(u+v) (where k=const)

Explanation:

In this question, one is expected to find the angle between u and v, and to get this angle, I will use the triangle formula.

|u-v|^2 = |u|^2 + |v|^2 - 2*|u|*|v|*cosθ

(2√2)² = (2√2)² + (2√2)² - 2(2√2)*(2√2)*cosθ

Expanding (2√2)² = (2√2)*(2√2) = 2*2*2 = 8

8 = 8 + 8 - 16*cosθ

8 = 16 - 16*cosθ

8 - 16 = -16*cosθ

-8 = -16*cosθ

cosθ = 8/16 = 1/2 = 0.5

θ = cos^(-1) (0.5)

θ = π/3

The angle between u and v is π/3 and parallel-to u plus v parallel-to = k*(u+v) (where k=const)