Question

given vectors \\(\mathbf{u} = \langle -2, 3 \
angle\\) and \\(\mathbf{v} = \langle 8, 5 \
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 \(\mathbf{u}=\langle - 2,3
angle\), we have \(u_1=-2\) and \(u_2 = 3\). For \(\mathbf{v}=\langle8,5
angle\), we have \(v_1 = 8\) and \(v_2=5\).

Step3: Calculate the sum

Using the vector addition rule:
\(u_1 + v_1=-2 + 8=6\)
\(u_2 + v_2=3 + 5 = 8\)
So \(\mathbf{u}+\mathbf{v}=\langle6,8
angle\)

Answer:

\(\langle 6, 8
angle\)