JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 17 March 2021, Shift 2, Maths Q89

Question 89 of 90 in this shift, Maths question 29 of 30, Section B.

Let

\overrightarrow{x}

be a vector in the plane containing vectors

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

and

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

. If the vector

\overrightarrow{x}

is perpendicular to

\left(3\hat{i}+2\hat{j}-\hat{k}\right)

and its projection on

\overrightarrow{a}

\frac{17\sqrt{6}}{2}

, then the value of

\left|\overrightarrow{x}\right|^2

is equal to __________.

Official answer

486

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.