JEE Main 2023 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 6 April 2023, Shift 1, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

Let 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

-2\hat i+\lambda\hat j+4\hat k

and

-\hat i+5\hat j+6\hat k

. Let the set

S=\{\lambda\in\mathbb{R}:

the points A, B, C and D are coplanar

\}

. Then

\sum_{\lambda\in S}(\lambda+2)^2

is equal to

(1)13
(2)25
(3)41Official answer
(4) $\frac{37}{2}$

Official answer

Option 3

NTA final key.

Chapter: Vector Algebra
Topic: Triple Products
Idea tested: Coplanarity of Four Points

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
8 Apr 2023, Shift 2 · Q16Let the vectors $\vec{u}_1 = \hat{i} + \hat{j} + a\hat{k}$ , $\vec{u}_2 = \hat{i} + b\hat{j} + \hat{k}$ and…HardSingle 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.