Question

Can someone help me?!!!!!

Answer 1

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

$(-3\cdot (-6), -2 \cdot (-6))=(18,12)$

The magnitude is given by Pythagorean's theorem:

$m=\sqrt{18^2+12^2}=21.6$

and the direction is given by the arctan of the ratio between the y-component and the x-component:

$\theta = tan^{-1} (\frac{12}{18})=33.7^{\circ}$