Vector A is added to a second vector B which has an x-component of 3 m and a y- component of -5 m. The resultant (A + B) is in the negative x direction and has a magnitude of 4 m. Find the magnitude and direction of A.

Explanation:

As B has a y component of -5, A must have a y component of 5 to have the result lie on the x axis.

As B has an x component of 3 and the result has an x component of -4, A must have an x component of -7

A = (-7, 5)

magnitude A = √(7² + 5²) = √74  ≈ 8.60

θ = arctan(y/x) = arctan(5/-7) ≈ 144.46° CCW from the positive x axis