Mathematics · Vector Algebra

JEE Main 2024 — 27 January, Shift 2 — Question 16

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 :

Option A:
49
Option B:
42
Option C:
50
Option D:
45
Correct

Answer: D

Step-by-step solution

$\mathrm{AB}=5$

$A C=5$

$\therefore \mathrm{D}$ is midpoint of BC

$\mathrm{D}\left(\frac{1}{2}, \frac{3}{2}, 3\right)$

$\therefore l=\sqrt{\left(2-\frac{1}{2}\right)^{2}+\left(-3-\frac{3}{2}\right)^{2}+(3-3)^{2}}$

$l=\sqrt{\frac{45}{2}}$

$\therefore 2 l^{2}=45$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 27 January, Shift 2
Subject: Mathematics
Chapter: Vector Algebra
Topic: Section Formula in Vectors