Question

given vectors \\(\mathbf{u} = \langle 7, -5 \
angle\\) and \\(\mathbf{v} = \langle 3, 6 \
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 \(\mathbf{u}=\langle 7, - 5
angle\), we have \(u_1 = 7\), \(u_2=-5\). For \(\mathbf{v}=\langle 3,6
angle\), we have \(v_1 = 3\), \(v_2 = 6\).

Step3: Add the corresponding components

Calculate the sum of the \(x\)-components: \(7 + 3=10\).
Calculate the sum of the \(y\)-components: \(-5+6 = 1\).

So, \(\mathbf{u}+\mathbf{v}=\langle10,1
angle\).

Answer:

\(\langle 10, 1
angle\)