Question

given vector $\mathbf{v}=\langle 3,1\
angle$, find $4\mathbf{v}$ graphically by stretching the vector by its tip and then writing the result in component form.

Explanation:

Step1: Multiply each component by 4

Given \(\mathbf{v}=\langle3,1
angle\). To find \(4\mathbf{v}\), we use the scalar - vector multiplication rule \(\text{If }\mathbf{v}=\langle a,b
angle\text{, then }k\mathbf{v}=\langle ka,kb
angle\).
So, for \(k = 4\), \(a = 3\), and \(b = 1\), we have \(4\mathbf{v}=\langle4\times3,4\times1
angle\).

Step2: Calculate the components

\(4\times3=12\) and \(4\times1 = 4\).

Answer:

\(\langle12,4
angle\)