JEE Main 2023 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 6 April 2023, Shift 2, Maths Q17

Question 17 of 90 in this shift, Maths question 17 of 30, Section A.

The sum of all values of

\alpha

, for which the points whose position vectors are

\hat{i}-2\hat{j}+3\hat{k}

2\hat{i}-3\hat{j}+4\hat{k}

(\alpha+1)\hat{i}+2\hat{k}

and

9\hat{i}+(\alpha-8)\hat{j}+6\hat{k}

are coplanar, is equal to

(1) $-2$
(2) $2$ Official answer
(3) $4$
(4) $6$

Official answer

Option 2

NTA final key.

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

Same idea in other shifts

Asked 5× in all

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
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
29 Jul 2022, Shift 2 · Q15If $(2, 3, 9)$ , $(5, 2, 1)$ , $(1, \lambda, 8)$ and $(\lambda, 2, 3)$ are coplanar, then the product of all possible values of $\lambda$ is :MediumSingle correct
26 Feb 2021, Shift 1 · Q62If $(1, 5, 35)$ , $(7, 5, 5)$ , $(1, \lambda, 7)$ and $(2\lambda, 1, 2)$ are coplanar, then the sum of all possible values of $\lambda$ is :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.