JEE Main 2026 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 2 April 2026, Shift 2, Maths Q14

Question 14 of 75 in this shift, Maths question 14 of 25, Section A.

Let the vectors

\vec{a} = -\hat{i} + \hat{j} + 3\hat{k}

and

\vec{b} = \hat{i} + 3\hat{j} + \hat{k}

. For some

\lambda, \mu \in \mathbb{R}

, let

\vec{c} = \lambda\vec{a} + \mu\vec{b}

. If

\vec{c} \cdot (3\hat{i} - 6\hat{j} + 2\hat{k}) = 10

and

\vec{c} \cdot (\hat{i} + \hat{j} + \hat{k}) = -2

, then

|\vec{c}|^2

is equal to:

(1) $8$
(2) $12$ Official answer
(3) $14$
(4) $15$

Official answer

Option 2

NTA final key.

Chapter: Vector Algebra
Topic: Dot Product
Idea tested: Solving Unknown Vector via Dot Products

Same topic in other shifts

All Dot Product questions

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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.