Question

given vectors \\(\mathbf{u} = \langle -8, 1 \
angle\\) and \\(\mathbf{v} = \langle 5, 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 \(\mathbf{u}=\langle - 8,1
angle\), we have \(u_1=-8\) and \(u_2 = 1\). For \(\mathbf{v}=\langle5,8
angle\), we have \(v_1 = 5\) and \(v_2=8\).

Step3: Calculate the sum of components

Calculate the sum of the \(x\)-components: \(u_1 + v_1=-8 + 5=-3\).
Calculate the sum of the \(y\)-components: \(u_2 + v_2=1+8 = 9\).

Step4: Write the resultant vector

Using the vector addition rule, \(\mathbf{u}+\mathbf{v}=\langle-3,9
angle\).

Answer:

\(\langle - 3,9
angle\)