Question

Can someone help me?!!!!!

Answer 1

magnitude: 21.6; direction: 33.7 degrees

Step-by-step 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=√(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) ((12)/(18))=33.7^(\circ)`