JEE Main 2023 · MathsMultiple choiceSingle correctMediumConceptual

JEE Main 10 April 2023, Shift 2, Maths Q17

Question 17 of 90 in this shift, Maths question 17 of 30, Section A.

If the points P and Q are respectively the circumcenter and the orthocentre of a

\Delta ABC

, then

\overrightarrow{PA} + \overrightarrow{PB} + \overrightarrow{PC}

is equal to

(1) $2\overrightarrow{QP}$
(2) $\overrightarrow{QP}$
(3) $\overrightarrow{PQ}$ Official answer
(4) $2\overrightarrow{PQ}$

Official answer

Option 3

NTA final key.

Chapter: Vector Algebra
Topic: Dot Product
Idea tested: Orthocenter Position Vector Relations

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