Question

If \(\overline{AB}=\overline{i}+\overline{j}-2\overline{k}\), \(\overline{CB}=2\overline{i}-\overline{j}+\alpha\overline{k}\) \((\alpha\in Z)\) are two sides of a triangle ABC and the angle between these two sides is \(\frac{\pi}{3}\), then the length of its third side is:

• A. \(6\)
• B. \(2\sqrt{6}\)
• C. \(\sqrt{6}\)
• D. \(3\sqrt{6}\)

Hint:

For triangle vector problems, always convert sides using position vectors and apply \(\overrightarrow{AC}=\overrightarrow{AB}-\overrightarrow{CB}\).

Answer 1

The Correct Option is B