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 option:

Find the value of $\lambda$:

Given, $\lambda (3i+2j-6k)=1$

$\Rightarrow$ $\lambda \left|3i+2j-6k\right|=1$

$\Rightarrow$$\lambda \sqrt{3^2+2^2+{\left(-6\right)}^2}=1$

$\Rightarrow$ $\lambda \sqrt{9+4+36}=1$

$\Rightarrow$ $\lambda \sqrt{49}=1$

$\Rightarrow$ $\lambda \times \pm 7=1$

$\mathbf{\therefore }\mathit{\lambda }\mathbf{}\mathbf{=}\mathbf{}\mathbf{\pm }\frac{\mathbf{1}}{\mathbf{7}}$

Hence, Option ‘A’ is Correct.