Question

If $\mathbf{a}$ is a non-zero vector of modulus a and m is a non-zero scalar, then $m\mathbf{a}$ is a unit vector if

• A. $m = \pm 1$
• B. $m = |\mathbf{a}|$
• C. $m = \frac{1}{|\mathbf{a}|}$
• D. $m = \pm 2$

Answer 1

Answer: (C)

$m = \frac{1}{|\mathbf{a}|}$

Answer 2

As $m\mathbf{a}$ is a unit vector, $|m\mathbf{a}| = 1$ ⇒ $|m||\mathbf{a}| = 1$

⇒ $|m| = \frac{1}{|\mathbf{a}|}$ ⇒ $m = \pm \frac{1}{|\mathbf{a}|}$