Question

The position vector of A and B are: \[ 2\hat{i} + 2\hat{j} + \hat{k} \quad \text{and} \quad 2\hat{i} + 4\hat{j} + 4\hat{k} \] The length of the internal bisector of \( \triangle AOB \) is:

• A. \( \frac{\sqrt{136}}{9} \)
• B. \( \frac{\sqrt{136}}{3} \)
• C. \( \frac{20}{3} \)
• D. \( \frac{217}{9} \)

Hint:

Use vector geometry and bisector length formulas to find distances and angles in triangles.

Answer 1

The Correct Option is A

Using the vector and geometry properties, the length of the internal bisector can be calculated. The formula gives the result as \( \frac{\sqrt{136}}{9} \).
Final Answer: \[ \boxed{\frac{\sqrt{136}}{9}} \]