The position vectors of the vertices A, B and C of a triangle are 2 i-3 j+3 k, 2 i+2 j+3 k and -i+j+3 k respectively. Let l denotes the length of the angle bisector AD of BAC where D is on the line segment BC, then 2 l² equals:

Vector Algebra: JEE Main 2024 Mathematics question

JEE Main 2024 · 27 Jan, Evening shift · Q5703

JEE Main 202427 Jan, Evening shiftMathematicsMediumVector Algebra184× since 2002

The position vectors of the vertices

\mathrm{A}, \mathrm{B}

and

\mathrm{C}

of a triangle are

2 \hat{i}-3 \hat{j}+3 \hat{k}, 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

\mathrm{AD}

\angle \mathrm{BAC}

where

\mathrm{D}

is on the line segment

\mathrm{BC}

, then

2 l^2

equals :