jee-main 2024 Q77

jee-main · India · session1_01feb_shift2 Vectors 3D & Lines Section Division and Coordinate Computation

Consider a $\triangle ABC$ where $A(1,3,2)$, $B(-2,8,0)$ and $C(3,6,7)$. If the angle bisector of $\angle BAC$ meets the line $BC$ at $D$, then the length of the projection of the vector $\overrightarrow{AD}$ on the vector $\overrightarrow{AC}$ is:
(1) $\frac{37}{2\sqrt{38}}$
(2) $\frac{\sqrt{38}}{2}$
(3) $\frac{39}{2\sqrt{38}}$
(4) $\sqrt{19}$

Consider a $\triangle ABC$ where $A(1,3,2)$, $B(-2,8,0)$ and $C(3,6,7)$. If the angle bisector of $\angle BAC$ meets the line $BC$ at $D$, then the length of the projection of the vector $\overrightarrow{AD}$ on the vector $\overrightarrow{AC}$ is:\\
(1) $\frac{37}{2\sqrt{38}}$\\
(2) $\frac{\sqrt{38}}{2}$\\
(3) $\frac{39}{2\sqrt{38}}$\\
(4) $\sqrt{19}$

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