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: Multiply each component by 2

Given \( \mathbf{v}=\langle - 2,1
angle\), to find \(2\mathbf{v}\), we use the scalar - vector multiplication rule \(k\langle a,b
angle=\langle ka,kb
angle\).
For \(k = 2\), \(a=-2\), and \(b = 1\), we have \(2\mathbf{v}=2\langle - 2,1
angle=\langle2\times(-2),2\times1
angle\)

Step2: Calculate the components

\(2\times(-2)=-4\) and \(2\times1 = 2\)

Answer:

\(\langle - 4,2
angle\)