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3D Geometry question

2024 · 29 Jan · Shift 1 · Q41

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JEE Main
Mathematics
3D Geometry
2024 · 29 Jan · Shift 1 · Q41

3D Geometry question

2024 · 29 Jan · Shift 1 · Q41

JEE MainMathematics3D GeometryMCQ+4 / −1

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

A
$\frac{3}{2} \sqrt{34}$
B
$\frac{2}{3} \sqrt{31}$
C
$\frac{2}{3} \sqrt{34}$
D
$\frac{3}{2} \sqrt{31}$

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