Question

let \\( \mathbf{w} = \overrightarrow{or} \\) where \\( o(-5, 6) \\) and \\( r(4, -2) \\). what is the component form of \\( \frac{1}{5}\mathbf{w} \\)?
\\( \langle -0.2, 0.8 \
angle \\)
\\( \langle -5, 20 \
angle \\)
\\( \langle 1.8, -1.6 \
angle \\)
\\( \langle 45, -40 \
angle \\)

Explanation:

Step1: Find the component form of \(\vec{OR}\)

If \(O(x_1,y_1)=(-5,6)\) and \(R(x_2,y_2)=(4,-2)\), then \(\vec{OR}=\langle x_2 - x_1,y_2 - y_1
angle\).
\(\vec{OR}=\langle4-(-5),-2 - 6
angle=\langle4 + 5,-2-6
angle=\langle9,-8
angle\)

Step2: Calculate \(\frac{1}{5}\vec{w}\)

If \(\vec{w}=\langle9,-8
angle\), then \(\frac{1}{5}\vec{w}=\frac{1}{5}\langle9,-8
angle=\langle\frac{9}{5},\frac{-8}{5}
angle\)
\(\frac{9}{5}=1.8\) and \(\frac{-8}{5}=-1.6\)

Answer:

\(\langle1.8,-1.6
angle\) (corresponding to the third option)