Answer:
magnitude: 21.6; direction: 33.7 degrees
Explanation:
When we multiply a vector by a scalar, we have to multiply each component of the vector by the scalar number. In this case, we have
vector: (-3,-2)
Scalar: -6
so the vector multiplied by the scalar will have components
[tex](-3\cdot (-6), -2 \cdot (-6))=(18,12)[/tex]
The magnitude is given by Pythagorean's theorem:
[tex]m=\sqrt{18^2+12^2}=21.6[/tex]
and the direction is given by the arctan of the ratio between the y-component and the x-component:
[tex]\theta = tan^{-1} (\frac{12}{18})=33.7^{\circ}[/tex]
