JEE Main 2025 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 3 April 2025, Shift 1, Maths Q24

Question 24 of 75 in this shift, Maths question 24 of 25, Section B.

Let

\vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = 3\hat{i} + 2\hat{j} - \hat{k}, \vec{c} = \lambda\hat{j} + \mu\hat{k}

and

\hat{d}

be a unit vector such that

\vec{a} \times \hat{d} = \vec{b} \times \hat{d}

and

\vec{c}\cdot\hat{d} = 1

. If

\vec{c}

is perpendicular to

\vec{a}

, then

\left|3\lambda\hat{d} + \mu\vec{c}\right|^2

is equal to ______

Official answer

NTA final key.

Chapter: Vector Algebra
Topic: Cross Product
Idea tested: Condition for Parallel Vectors

Same topic in other shifts

All Cross 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 42 of the 174 JEE Main shifts held from 2017 to 2026.