Question

How to find out the values of p and q?

Answer 1

Part a

Comparing the
`\vec{i}` components,
`(p+14)/2=9 \implies \boxed{p=4}`

Comparing the
`\vec{j}` components,
`(8+q)/2=40 \implies \boxed{q=72}`

Part B

`\overrightarrow{OM}=9\vec{i}+40\vec{j} \implies \left|\overrightarrow{OM}\right|=√(9^2 +40^2)=41\\\\`
Dividing each of the components of
`\overrightarrow{OM}` by this magnitude, the unit vector is
`\boxed{(9)/(41)\vec{i}+(40)/(41)\vec{j}}`.