Scalar multiplication

Example 1

Vector $\vec{v}$ has magnitude of 3 units and creates an angle of $160^{\circ }$ with the positive $x$–axis.

Task. Find the magnitude and direction of $5\vec{v}$.
Give the direction as an angle measure between $0^{\circ }$ and $360^{\circ }$.

In the sketch you drew, you treated

and then wrote

SVG (your sketch)

Example 2

Vector $\vec{v}$ has magnitude $4$ units at angle $80^{\circ }$ from the positive $x$–axis.

Task. Find the magnitude and direction of $-\frac{1}{2}\vec{v}$.

From your working:

direction $\approx 260^{\circ }$.

SVG (your sketch)