Question

given vectors \\(\mathbf{u} = \langle 4, 8 \
angle\\) and \\(\mathbf{v} = \langle 1, -7 \
angle\\), find the sum \\(\mathbf{u} + \mathbf{v}\\) and write the result in component form.

Explanation:

Step1: Recall vector addition rule

To add two vectors \(\mathbf{u}=\langle u_1, u_2
angle\) and \(\mathbf{v}=\langle v_1, v_2
angle\), we use the rule \(\mathbf{u}+\mathbf{v}=\langle u_1 + v_1, u_2 + v_2
angle\).

Step2: Substitute the components

Given \(\mathbf{u}=\langle 4, 8
angle\) and \(\mathbf{v}=\langle 1, -7
angle\), we substitute \(u_1 = 4\), \(u_2 = 8\), \(v_1 = 1\), and \(v_2=-7\) into the formula.
So, \(u_1 + v_1=4 + 1 = 5\) and \(u_2 + v_2=8+(-7)=8 - 7 = 1\).

Answer:

\(\langle 5, 1
angle\)