Let for a triangle ABC, $\overrightarrow{AB}=-2\hat{i}+\hat{j}+3\hat{k}$ $\overrightarrow{CB}=\alpha\hat{i}+\beta\hat{j}+\gamma\hat{k}$ $\overrightarrow{CA}=4\hat{i}+3\hat{j}+\delta\hat{k}$ If $\delta>0$ and the area of the triangle ABC is $5\sqrt{6}$, then $\overrightarrow{CB}\cdot\overrightarrow{CA}$ is equal to

JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 13 April 2023, Shift 2, Maths Q18

Question 18 of 90 in this shift, Maths question 18 of 30, Section A.

Let for a triangle ABC,

\overrightarrow{AB}=-2\hat{i}+\hat{j}+3\hat{k}

\overrightarrow{CB}=\alpha\hat{i}+\beta\hat{j}+\gamma\hat{k}

\overrightarrow{CA}=4\hat{i}+3\hat{j}+\delta\hat{k}

\delta>0

and the area of the triangle ABC is

5\sqrt{6}

, then

\overrightarrow{CB}\cdot\overrightarrow{CA}

is equal to

(1) $60$ Official answer
(2) $54$
(3) $120$
(4) $108$

Official answer

Option 1

NTA final key.

Chapter: Vector Algebra
Topic: Cross Product
Idea tested: Area of Triangles and Parallelograms

Same idea in other shifts

Asked 4× in all

6 Apr 2026, Shift 2 · Q15Let $\vec{a}=2\hat{i}+3\hat{j}+3\hat{k}$ and $\vec{b}=6\hat{i}+3\hat{j}+3\hat{k}$ . Then the square of the area of the triangle with…EasySingle correct
2 Apr 2025, Shift 1 · Q5Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutually perpendicular. Let the areas of the triangles ABC, ACD and ADB be…MediumSingle correct
9 Apr 2024, Shift 1 · Q18Let three vectors $\vec{a}=\alpha\hat{i}+4\hat{j}+2\hat{k}$ , $\vec{b}=5\hat{i}+3\hat{j}+4\hat{k}$ , $\vec{c}=x\hat{i}+y\hat{j}+z\hat{k}$ …MediumSingle correct

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 42 of the 174 JEE Main shifts held from 2017 to 2026.