Question

given vectors \\( \mathbf{u} = \langle 8, 8 \
angle \\) and \\( \mathbf{v} = \langle -8, -4 \
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: Identify components of vectors

For \(\mathbf{u}=\langle 8, 8
angle\), we have \(u_1 = 8\) and \(u_2 = 8\). For \(\mathbf{v}=\langle - 8,-4
angle\), we have \(v_1=-8\) and \(v_2 = - 4\).

Step3: Add the corresponding components

Calculate the sum of the \(x\)-components: \(u_1 + v_1=8+( - 8)=0\).
Calculate the sum of the \(y\)-components: \(u_2 + v_2=8+( - 4)=4\).

Answer:

\(\langle 0, 4
angle\)