Question

given vectors \\(\mathbf{u} = \langle -6, 2 \
angle\\) and \\(\mathbf{v} = \langle 7, -8 \
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 \(\mathbf{u}=\langle - 6,2
angle\), \(u_1=-6\) and \(u_2 = 2\). For \(\mathbf{v}=\langle7,-8
angle\), \(v_1 = 7\) and \(v_2=-8\).

Step3: Add the corresponding components

Calculate the sum of the \(x\)-components: \(-6 + 7=1\).
Calculate the sum of the \(y\)-components: \(2+(-8)=2 - 8=-6\).
So, \(\mathbf{u}+\mathbf{v}=\langle1,-6
angle\).

Answer:

\(\langle1, - 6
angle\)