JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 22 July 2021, Shift 2, Maths Q80

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

Let a vector

\vec{\mathrm{a}}

be coplanar with vectors

\vec{\mathrm{b}}=2\hat{i}+\hat{j}+\hat{k}

and

\vec{\mathrm{c}}=\hat{i}-\hat{j}+\hat{k}

. If

\vec{\mathrm{a}}

is perpendicular to

\vec{\mathrm{d}}=3\hat{i}+2\hat{j}+6\hat{k}

, and

|\vec{\mathrm{a}}|=\sqrt{10}

. Then a possible value of

[\vec{\mathrm{a}}\ \vec{\mathrm{b}}\ \vec{\mathrm{c}}]+[\vec{\mathrm{a}}\ \vec{\mathrm{b}}\ \vec{\mathrm{d}}]+[\vec{\mathrm{a}}\ \vec{\mathrm{c}}\ \vec{\mathrm{d}}]

is equal to :

(1) $-40$
(2) $-42$ Official answer
(3) $-38$
(4) $-29$

Official answer

Option 2

NTA final key.

Chapter: Vector Algebra
Topic: Triple Products
Idea tested: STP Algebraic Properties

Same topic in other shifts

All Triple Products questions

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.