JEE Main 2022 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 29 July 2022, Shift 2, Maths Q15

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

(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 :

(1) $\frac{21}{2}$
(2) $\frac{59}{8}$
(3) $\frac{57}{8}$
(4) $\frac{95}{8}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Three Dimensional Geometry
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
6 Apr 2023, Shift 2 · Q17The sum of all values of $\alpha$ , for which the points whose position vectors are $\hat{i}-2\hat{j}+3\hat{k}$ ,…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
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.