JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 26 July 2022, Shift 2, Maths Q22

Question 22 of 90 in this shift, Maths question 22 of 30, Section B.

The largest value of

a

, for which the perpendicular distance of the plane containing the lines

\vec{r}=(\hat{i}+\hat{j})+\lambda(\hat{i}+a\hat{j}-\hat{k})

and

\vec{r}=(\hat{i}+\hat{j})+\mu(-\hat{i}+\hat{j}-a\hat{k})

from the point

(2,1,4)

\sqrt{3}

, is ________.

Official answer

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Plane Containing Two Lines

Same idea in other shifts

Asked 4× in all

26 Jun 2022, Shift 2 · Q15If the lines $\vec{r} = (\hat{i} - \hat{j} + \hat{k}) + \lambda(3\hat{j} - \hat{k})$ and…MediumSingle correct
2 Sep 2020, Shift 2 · Q67A plane passing through the point $(3,\,1,\,1)$ contains two lines whose direction ratios are $1,\,-2,\,2$ and $2,\,3,\,-1$ respectively.…MediumSingle correct
3 Sep 2020, Shift 2 · Q75Let a plane P contain two lines $\vec{r} = \hat{i} + \lambda(\hat{i} + \hat{j})$ , $\lambda \in \mathbf{R}$ and…MediumNumerical value

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.