Question

given vector $\mathbf{v}=\langle 2,1\
angle$, find $-2\mathbf{v}$ graphically by stretching the vector by its tip and then writing the result in component form.

Explanation:

Step1: Recall scalar - vector multiplication rule

If \(\mathbf{v}=\langle a,b
angle\) and \(k\) is a scalar, then \(k\mathbf{v}=\langle ka,kb
angle\). Here \(\mathbf{v}=\langle 2,1
angle\) and \(k = - 2\).

Step2: Calculate the components

For the \(x\) - component: \(ka=-2\times2=-4\).
For the \(y\) - component: \(kb=-2\times1=-1\).

Answer:

\(\langle - 4,-2
angle\)