Question

If $\vec{P}=3 \hat{i}+\sqrt{3} \hat{j}+2 \hat{k}$ and $\vec{Q}=4 \hat{i}+\sqrt{3} \hat{j}+25 \hat{k}$ then, The unit vector in the direction of $\vec{P} \times \vec{Q}$ is $\frac{1}{x}(\sqrt{3} i+\hat{j}-2 \sqrt{3} \hat{k})$ The value of $x$ is

Answer 1

The correct answer is 4.
P×Q​=∣∣​i^34​j^​3​3​​k^22.5​∣∣​=3​2i^​+2j^​​−3​k^

⇒∣P×Q​∣P×Q​​=21​(3​2i^​+2j^​​−3​k^)

=41​(3​i^+j^​−23​k^)x=4