Question

Type the correct answer in each box. Round your answers to two decimal places. Subtract vector v = <2, -3> from vector u = <5, 2>. The magnitude of the resulting vector, u – v, is approximately___ , and its angle of direction is approximately___ .

Answer 1

u - v = <5, 2> - <2, - 3> = <5 - 2, 2 + 3> = <3, 5>

given a vector <u, v> then the magnitude is √ (u² + v² ) and it's angle of direction is

θ = $tan^{-1}$($\frac{v}{u}$)

thus the magnitude of <3, 5> = √(3² + 5²) = √34 ≈ 5.83 ( to 2 dec. places )

Θ = $tan^{-1}$($\frac{5}{3}$) = 59.04° ( to 2 dec. places )