JEE MAIN - Mathematics (2024 - 29th January Morning Shift - No. 11)
Let $$O$$ be the origin and the position vectors 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 $$\angle \mathrm{AOB}$$ meets the line $$\mathrm{AB}$$ at $$\mathrm{C}$$, then the length of $$O C$$ is
$$\frac{3}{2} \sqrt{34}$$
$$\frac{2}{3} \sqrt{31}$$
$$\frac{2}{3} \sqrt{34}$$
$$\frac{3}{2} \sqrt{31}$$
Explanation
_29th_January_Morning_Shift_en_11_1.png)
$$\text { length of } O C=\frac{\sqrt{136}}{3}=\frac{2 \sqrt{34}}{3}$$
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