JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 29 January 2024, Shift 1, Maths Q18

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

Let O be the origin and the position vectors of A and B be

2\hat{i}+2\hat{j}+\hat{k}

and

2\hat{i}+4\hat{j}+4\hat{k}

respectively. If the internal bisector of

\angle AOB

meets the line AB at C, then the length of OC is

(1) $\frac{2}{3}\sqrt{34}$ Official answer
(2) $\frac{3}{2}\sqrt{34}$
(3) $\frac{2}{3}\sqrt{31}$
(4) $\frac{3}{2}\sqrt{31}$

Official answer

Option 1

NTA final key.

Chapter: Vector Algebra
Topic: Dot Product
Idea tested: Angle Bisector Construction

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.