Question

given vectors \\(\mathbf{u} = \langle -8, -7 \
angle\\) and \\(\mathbf{v} = \langle 5, -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 \(\mathbf{u}+\mathbf{v}=\langle u_1 + v_1, u_2 + v_2
angle\).
Here, \(u_1=-8\), \(u_2 = - 7\), \(v_1 = 5\), and \(v_2=-5\).

Step2: Calculate the x - component

For the x - component of the sum, we add the x - components of \(\mathbf{u}\) and \(\mathbf{v}\): \(u_1 + v_1=-8 + 5=-3\).

Step3: Calculate the y - component

For the y - component of the sum, we add the y - components of \(\mathbf{u}\) and \(\mathbf{v}\): \(u_2 + v_2=-7+(-5)=-12\).

Answer:

\(\langle - 3,-12
angle\)