Consider a $\Delta ABC$ 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 :

Option 2: $\frac{37}{2\sqrt{38}}$

JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 1 February 2024, Shift 2, Maths Q17

Question 17 of 90 in this shift, Maths question 17 of 30, Section A.

Consider a

\Delta 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

D

, then the length of the projection of the vector

\overrightarrow{AD}

on the vector

\overrightarrow{AC}

is :

(1) $\sqrt{19}$
(2) $\frac{37}{2\sqrt{38}}$ Official answer
(3) $\frac{\sqrt{38}}{2}$
(4) $\frac{39}{2\sqrt{38}}$

Official answer

Option 2

NTA final key.

Chapter: Vector Algebra
Topic: Dot Product
Idea tested: Scalar and Vector Projection

Same idea in other shifts

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.