Vector A has a magnitude of 5.0 m and points east, vector B has a magnitude of 2.0 m and points north, and vector C has a magnitude of 7.0 m and points west. The resultant vector A + B + C is given by

The answer to your question is     Vr = 2.83 m, to the Northwest

Explanation:

Data

Vector A = 5 m

Vector B = 2.0 m

Vector C = 7.0 m

Process

1.- Calculate the ∑Vx and ∑Vy

∑Vx = 5m - 7m = -2m    Vectors substract because they are in opposite directions

∑Vy = 2m

2.- Calculate the resultant vector with the Pythagorean theorem

      Vr² = Vx² + Vy²

      Vr² = (-2)² + (2)²

     Vr² = 4 + 4

     Vr² = 8

     Vr = 2.83 m

3.- Calculate the direction

tan Ф = 2/-2 = 1

tan⁻¹Ф = 45°  to the Northwest