Question

$\overrightarrow{A}$ and $\overrightarrow{B}$ are vectors, and $\theta$ is the angle between them. What can you do to maximize $\overrightarrow{A}\cdot \overrightarrow{B}$ ?
I. Maximize the magnitude of A
II. Maximize the magnitude of B
III. Set to ${90}^o$

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

Answer 1

Answer: (D)

I and II only

The dot product of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is given by

$\overrightarrow{A}.\overrightarrow{B}=ABcos\theta$

It can be maximized by maximizing the magnitude of either or both A and B, and also by making $\theta =0^{\circ }$