jee-main 2024 Q77

jee-main · India · session1_27jan_shift2 Vectors 3D & Lines Section Division and Coordinate Computation
The position vectors of the vertices $A , B$ and $C$ of a triangle are $2 \hat { i } - 3 \hat { j } + 3 \hat { k } , \quad 2 \hat { i } + 2 \hat { j } + 3 \hat { k }$ and $- \hat { i } + \hat { j } + 3 \hat { k }$ respectively. Let $l$ denotes the length of the angle bisector AD of $\angle \mathrm { BAC }$ where D is on the line segment BC , then $2 l ^ { 2 }$ equals :
(1) 49
(2) 42
(3) 50
(4) 45
The position vectors of the vertices $A , B$ and $C$ of a triangle are $2 \hat { i } - 3 \hat { j } + 3 \hat { k } , \quad 2 \hat { i } + 2 \hat { j } + 3 \hat { k }$ and $- \hat { i } + \hat { j } + 3 \hat { k }$ respectively. Let $l$ denotes the length of the angle bisector AD of $\angle \mathrm { BAC }$ where D is on the line segment BC , then $2 l ^ { 2 }$ equals :\\
(1) 49\\
(2) 42\\
(3) 50\\
(4) 45