JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 18 March 2021, Shift 2, Maths Q66

Question 66 of 90 in this shift, Maths question 6 of 30, Section A.

In a triangle ABC, if

\left|\overrightarrow{BC}\right|=8

\left|\overrightarrow{CA}\right|=7

\left|\overrightarrow{AB}\right|=10

, then the projection of the vector

\overrightarrow{AB}

\overrightarrow{AC}

is equal to :

(1) $\frac{115}{16}$
(2) $\frac{85}{14}$ Official answer
(3) $\frac{127}{20}$
(4) $\frac{25}{4}$

Official answer

Option 2

NTA final key.

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

Same idea in other shifts

Asked 11× in all

2 Apr 2025, Shift 1 · Q11If $\vec{a}$ is a nonzero vector such that its projections on the vectors $2\hat{i}-\hat{j}+2\hat{k}$ , $\hat{i}+2\hat{j}-2\hat{k}$ and…MediumSingle correct
8 Apr 2024, Shift 2 · Q18Let $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}$ , $\vec{b} = 2\hat{i} + 3\hat{j} - 5\hat{k}$ and…MediumSingle correct
1 Feb 2024, Shift 2 · Q17Consider 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 $D$ ,…MediumSingle correct
25 Jul 2022, Shift 2 · Q17Let $\vec{a}=\hat{i}-\hat{j}+2\hat{k}$ and let $\vec{b}$ be a vector such that $\vec{a}\times\vec{b}=2\hat{i}-\hat{k}$ and…MediumSingle correct
30 Jul 2022, Shift 2 · Q88Let $OABC$ be a parallelogram, $O$ be the origin, $A\,(2, 4, -5)$ and $C\,(b, 2, 3)$ . If $P\,(a, a, a)$ and $Q\,(9-a^2, 3, a-1)$ ,…HardNumerical value
26 Jun 2022, Shift 2 · Q16Let $\vec{a} = \hat{i} + \hat{j} + 2\hat{k}$ , $\vec{b} = 2\hat{i} - 3\hat{j} + \hat{k}$ and $\vec{c} = \hat{i} - \hat{j} + \hat{k}$ be…MediumSingle correct
29 Jun 2022, Shift 1 · Q5Let $\vec{a} = \alpha\hat{i} + 3\hat{j} - \hat{k}$ , $\vec{b} = 3\hat{i} - \beta\hat{j} + 4\hat{k}$ and…MediumSingle correct
26 Aug 2021, Shift 2 · Q87If the projection of the vector $\hat{i}+2\hat{j}+\hat{k}$ on the sum of the two vectors $2\hat{i}+4\hat{j}-5\hat{k}$ and…EasyNumerical value

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.