Question

If $\lambda \left(3\hat{i}+2\hat{j}-6\hat{k}\right)$ 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

Answer: (A)

Now, $|(3\hat{i}+2\hat{j}-6\hat{k})|=\sqrt{3^2+2^2+(-6{)}^2}$
$=\sqrt{9+4+36}$
$=\sqrt{49}=7$
Since, $\lambda (3\hat{i}+2\hat{j}-6\hat{k})$ is a unit vector.
$\therefore \lambda =\pm \frac{1}{|3\hat{i}+2\hat{j}-6\hat{k}|}$
$=\pm \frac{1}{7}$