jee-main 2024 Q78

jee-main · India · session1_29jan_shift1 Vectors Introduction & 2D Section Ratios and Intersection via Vectors

Let $O$ be the origin and the position vector of $A$ and $B$ be $2 \hat { i } + 2 \hat { j } + \widehat { k }$ and $2 \hat { i } + 4 \hat { j } + 4 \widehat { k }$ respectively. If the internal bisector of $\angle A O B$ meets the line $A B$ at $C$, then the length of $O C$ is
(1) $\frac { 2 } { 3 } \sqrt { 31 }$
(2) $\frac { 2 } { 3 } \sqrt { 34 }$
(3) $\frac { 3 } { 4 } \sqrt { 34 }$
(4) $\frac { 3 } { 2 } \sqrt { 31 }$

Let $O$ be the origin and the position vector of $A$ and $B$ be $2 \hat { i } + 2 \hat { j } + \widehat { k }$ and $2 \hat { i } + 4 \hat { j } + 4 \widehat { k }$ respectively. If the internal bisector of $\angle A O B$ meets the line $A B$ at $C$, then the length of $O C$ is\\
(1) $\frac { 2 } { 3 } \sqrt { 31 }$\\
(2) $\frac { 2 } { 3 } \sqrt { 34 }$\\
(3) $\frac { 3 } { 4 } \sqrt { 34 }$\\
(4) $\frac { 3 } { 2 } \sqrt { 31 }$

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