Question

given vector $\mathbf{v}=\langle -3,1\
angle$, find $2\mathbf{v}$ graphically by stretching the vector by its tip and then writing the result in component form.

Explanation:

Step1: Multiply each component by 2

Given \(\mathbf{v}=\langle - 3,1
angle\), for \(2\mathbf{v}\), we use the scalar - vector multiplication rule \(k\langle a,b
angle=\langle ka,kb
angle\). Here \(k = 2\), \(a=-3\), \(b = 1\).
So, \(2\mathbf{v}=2\langle - 3,1
angle=\langle2\times(-3),2\times1
angle\)

Step2: Calculate the components

\(2\times(-3)=-6\) and \(2\times1 = 2\)

Answer:

\(\langle-6,2
angle\)