Question

given vectors \\(\mathbf{u} = \langle -1, -6 \
angle\\) and \\(\mathbf{v} = \langle 7, 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 formula \(\mathbf{u}+\mathbf{v}=\langle u_1 + v_1, u_2 + v_2
angle\).

Step2: Identify components of vectors

For \(\mathbf{u}=\langle - 1,-6
angle\), we have \(u_1=-1\) and \(u_2 = - 6\). For \(\mathbf{v}=\langle7,4
angle\), we have \(v_1 = 7\) and \(v_2=4\).

Step3: Add the corresponding components

Calculate the \(x\)-component: \(u_1 + v_1=-1 + 7=6\).
Calculate the \(y\)-component: \(u_2 + v_2=-6 + 4=-2\).

Answer:

\(\langle 6,-2
angle\)