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. $\pm7$
• 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} $