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

6 Apr 2024, Shift 2 · Q18Let $\vec{a}=2\hat{i}+\hat{j}-\hat{k}$ , $\vec{b}=\left(\left(\vec{a}\times(\hat{i}+\hat{j})\right)\times\hat{i}\right)\times\hat{i}$ . Then…MediumSingle correct
6 Apr 2023, Shift 1 · Q15Let the position vectors of the points A, B, C and D be $5\hat i+5\hat j+2\lambda\hat k$ , $\hat i+2\hat j+3\hat k$ ,…MediumSingle correct
25 Jul 2021, Shift 1 · Q71Let the vectors $(2+a+b)\hat{i}+(a+2b+c)\hat{j}-(b+c)\hat{k}$ , $(1+b)\hat{i}+2b\hat{j}-b\hat{k}$ and…MediumSingle correct
16 Mar 2021, Shift 2 · Q84Let $\vec c$ be a vector perpendicular to the vectors $\vec a=\hat i+\hat j-\hat k$ and $\vec b=\hat i+2\hat j+\hat k$ . If…MediumNumerical value
8 Jan 2020, Shift 1 · Q66Let the volume of a parallelopiped whose coterminous edges are given by $\vec{u}=\hat{i}+\hat{j}+\lambda\hat{k}$ ,…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.