Question

Two adjacent sides of a triangle are represented by the vectors $2\vec{i}+\vec{j}-2\vec{k}$ and $2\sqrt{3}\vec{i}-2\sqrt{3}\vec{j}+\sqrt{3}\vec{k}$. Then the least angle of the triangle and perimeter of the triangle are respectively

• A. $\frac{\pi}{3}; 3(3+\sqrt{3})$
• B. $\frac{\pi}{12}; 6+3\sqrt{2}$
• C. $\frac{\pi}{2}; 12$
• D. $\frac{\pi}{6}; 9+3\sqrt{3}$

Hint:

When given two vectors representing adjacent sides of a triangle, always calculate their dot product first. If it is zero, the triangle is right-angled, which simplifies finding the other sides and angles significantly.

Answer 1

The Correct Option is D