Three Dimensional Geometry Question 11
Question 11 - 2024 (29 Jan Shift 1)
Let $O$ be the origin and the position vector of $A$ and $B$ be $2 \hat{i}+2 \hat{j}+\hat{k}$ and $2 \hat{i}+4 \hat{j}+4 \hat{k}$ respectively. If the internal bisector of $\angle A O B$ meets the line $A B$ at $\mathrm{C}$, then the length of $\mathrm{OC}$ is
(1) $\frac{2}{3} \sqrt{31}$
(2) $\frac{2}{3} \sqrt{34}$
(3) $\frac{3}{4} \sqrt{34}$
(4) $\frac{3}{2} \sqrt{31}$
Show Answer
Answer (2)
Solution
length of $O C=\frac{\sqrt{136}}{3}=\frac{2 \sqrt{34}}{3}$
