Question

For the vectors u and v with magnitudes u = 88 and v = 99​, find the angle θ between u and v which makes u and v = 77.

Answer 1

89.5°

Explanation:

Using the vector formula
`u.v = |u||v|cos\theta`

|u| = magnitude of vector u

|v| = magnitude of vector v

u.v is the dot product of vector u and v

Given |u| = 88, |v| = 99 and u.v = 77, to get
`\theta` we will substitute the given values into the equation above;

`77 = 88*99cos\theta\\cos\theta = (77)/(88*99) \\cos\theta = (77)/(8712) \\cos\theta = 0.008838\\\theta = cos^(-1) 0.008838\\\theta = 89.5^(0)`