Question

if \\(\vec{v} = \langle 4, -8 \
angle\\) and \\(\vec{w} = \langle 5, 2 \
angle\\), find the difference \\(\vec{v} - \vec{w}\\). \\(\vec{v} - \vec{w} = \langle \square, \square \
angle\\)

Explanation:

Step1: Recall vector subtraction rule

To subtract two vectors \(\vec{v}=\langle v_1, v_2
angle\) and \(\vec{w}=\langle w_1, w_2
angle\), we use the rule \(\vec{v}-\vec{w}=\langle v_1 - w_1, v_2 - w_2
angle\).
Here, \(v_1 = 4\), \(v_2=-8\), \(w_1 = 5\), \(w_2 = 2\).

Step2: Calculate the x - component

For the x - component of \(\vec{v}-\vec{w}\), we compute \(v_1 - w_1\):
\(4-5=-1\)

Step3: Calculate the y - component

For the y - component of \(\vec{v}-\vec{w}\), we compute \(v_2 - w_2\):
\(-8 - 2=-10\)

Answer:

\(\vec{v}-\vec{w}=\langle - 1,-10
angle\)