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 \ -(√(2))/(2), 2-(√(2))/(2) \ \textgreater \`