JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 8 April 2023, Shift 2, Maths Q16

Question 16 of 90 in this shift, Maths question 16 of 30, Section A.

Let the vectors

\vec{u}_1 = \hat{i} + \hat{j} + a\hat{k}

\vec{u}_2 = \hat{i} + b\hat{j} + \hat{k}

and

\vec{u}_3 = c\hat{i} + \hat{j} + \hat{k}

be coplanar. If the vectors

\vec{v}_1 = (a + b)\hat{i} + c\hat{j} + c\hat{k}

\vec{v}_2 = a\hat{i} + (b + c)\hat{j} + a\hat{k}

and

\vec{v}_3 = b\hat{i} + b\hat{j} + (c + a)\hat{k}

are also coplanar, then

6(a + b + c)

is equal to

(1)0
(2)4
(3)6
(4)12Official answer

Official answer

Option 4

NTA final key.

Chapter: Vector Algebra
Topic: Triple Products
Idea tested: Parametric Coplanarity via STP

Same topic in other shifts

All Triple Products questions

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6 Apr 2023, Shift 2 · Q18Let the vectors $\vec{a},\vec{b},\vec{c}$ represent three coterminous edges of a parallelopiped of volume V. Then the volume of the…MediumSingle correct
11 Apr 2023, Shift 2 · Q17If four distinct points with position vectors $\vec{a}, \vec{b}, \vec{c}$ and $\vec{d}$ are coplanar, then $[\vec{a}\ \vec{b}\ \vec{c}]$ …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.