Question

If $\lambda (3i+2j-6k)$ is a unit vector, then the values of $\lambda$ are?

• A. $\pm \frac{1}{7}$
• B. $\pm 7$
• C. $\pm \sqrt{43}$
• D. $\pm \frac{1}{\sqrt{43}}$
• E. $\pm \frac{1}{\sqrt{7}}$

Answer 1

The correct option is A

$\pm \frac{1}{7}$

Explanation for the correct answer.

As $\lambda (3i+2j-6k)$ is a unit vector, so

$\begin{array}{rcl}\lambda & =& \frac{1}{\left|3i+2j-6k\right|}\\ & =& \frac{1}{\sqrt{3^2+2^2+{\left(-6\right)}^2}}\\ & =& \frac{1}{\sqrt{49}}\\ & =& \pm \frac{1}{7}\end{array}$

Hence, option A is correct.