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

[ \vec{v} = \langle 2,1\rangle \quad\Longrightarrow\quad 5\vec{v} = \langle 10,5\rangle ] and then wrote

[ 5+10 = 15 \text{ units.} ]

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

Task. Find the magnitude and direction of $-\dfrac12 \vec{v}$ .

From your working:

[ -\frac12 \vec{v} = (-0.5, -2) ] [ -0.5 - 2 = -2.5 ] [ \left\lVert -\frac12 \vec{v} \right\rVert = 2 \text{ units} ] direction $\approx 260^\circ$ .