Question

The angle between vectors $A$ and $B$ is $\theta$. If we want to maximise $A\hat{A}\cdot B$, What can we do?
I. Maximise the magnitude of $A$.
II. Maximise the magnitude of $B$.
III. Set $\theta$ to ${90}^0\hat{A}.$

• A. None of the above
• B. I only
• C. III only
• D. I and II only
• E. I, II, and III

Answer 1

Answer: (D)

I and II only

The resultant vector, $R=A\hat{A}.B=|A||B|cos\theta$

Thus either maximising $|A|$ or $|B|$ will maximise $R$.

Also $R{|}_{\theta ={90}^o}=|A||B|cos{90}^o=0$ $(\because cos{90}^o=0)$