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

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.