Question

Find the component form of v given the magnitudes of u and u + v and the angles that u and u + v make with the positive x-axis. u = 1, θ = 45° u + v = 2 , θ = 90°

Answer 1

Given |u| = 1 and a = 45, you can determine the component form of u.
$u = \ \textless \ cos(45),sin(45)\ \textgreater$

In same way you can find component form of u+v
$u+v = \ \textless \ 2cos(90), 2sin(90)\ \textgreater$

By property of vector subtraction:
v = (u+v) - u

$v = \ \textless \ 2cos(90) - cos(45), 2sin(90) - sin(45)\ \textgreater$
$v = \ \textless \ -\frac{\sqrt{2}}{2}, 2-\frac{\sqrt{2}}{2} \ \textgreater$