Question

A vector of components (−3, −2) is multiplied by the scalar value of -6. What is the magnitude and direction of the resultant vector?

Answer 1

The components of the resultant will be: (18, 12)

In order to find the magnitude you have to apply the Pythagorean theorem:
√(18² + 12²) = √468 = 21.6
Therefore, the magnitude of the resultant vector is 21.6

The direction is given by the formula:
α = tan⁻¹(v_y / v_x)
   = tan⁻¹(12/18)
   = 33.7°
Therefore, the direction will be 33.7° from the x-axis.