Question

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

Explanation:

Step1: Multiply each component by 3

Given \(\mathbf{v}=\langle3,-4
angle\), to find \(3\mathbf{v}\), we use the scalar - vector multiplication rule. If \(\mathbf{v}=\langle a,b
angle\), then \(k\mathbf{v}=\langle ka,kb
angle\). Here \(k = 3\), \(a = 3\), and \(b=-4\).

$$3\mathbf{v}=\langle3\times3,3\times(-4) angle$$

Step2: Calculate the components

$$3\times3 = 9$$

$$3\times(-4)=-12$$

Answer:

\(\langle9,-12
angle\)