JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 18 March 2021, Shift 1, Maths Q80

Question 80 of 90 in this shift, Maths question 20 of 30, Section A.

A vector

\vec{a}

has components 3p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to new system,

\vec{a}

has components

p+1

and

\sqrt{10}

, then a value of p is equal to :

(1)1
(2) $-1$ Official answer
(3) $\frac{4}{5}$
(4) $-\frac{5}{4}$

Official answer

Option 2

NTA final key.

Chapter: Vector Algebra
Topic: Dot Product
Idea tested: Dot Product Invariance Under Rotation

Same topic in other shifts

All Dot Product questions

2 Apr 2026, Shift 1 · Q14If $\vec a$ and $\vec b$ are two vectors such that $|\vec a|=2$ and $|\vec b|=3$ , then the maximum value of…HardSingle correct
2 Apr 2026, Shift 2 · Q14Let the vectors $\vec{a} = -\hat{i} + \hat{j} + 3\hat{k}$ and $\vec{b} = \hat{i} + 3\hat{j} + \hat{k}$ . For some…MediumSingle correct
2 Apr 2026, Shift 2 · Q16Two adjacent sides of a parallelogram $PQRS$ are given by $\vec{PQ} = \hat{j} + \hat{k}$ and $\vec{PS} = \hat{i} - \hat{j}$ . If the side…MediumSingle correct
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
7 Apr 2025, Shift 2 · Q15Let $\vec{a}$ and $\vec{b}$ be the vectors of the same magnitude such that…MediumSingle correct
8 Apr 2025, Shift 2 · Q14Let $\vec{a} = \hat{i} + 2\hat{j} + \hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} - \hat{k}$ . Let $\hat{c}$ be a unit vector in the plane of…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.