JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 June 2022, Shift 2, Maths Q15

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

If the lines

\vec{r} = (\hat{i} - \hat{j} + \hat{k}) + \lambda(3\hat{j} - \hat{k})

and

\vec{r} = (\alpha\hat{i} - \hat{j}) + \mu(2\hat{i} - 3\hat{k})

are co-planar, then the distance of the plane containing these two lines from the point

(\alpha, 0, 0)

is:

(1) $\frac{2}{9}$
(2) $\frac{2}{11}$ Official answer
(3) $\frac{4}{11}$
(4) $2$

Official answer

Option 2

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 Jul 2022, Shift 2 · Q22The largest value of $a$ , for which the perpendicular distance of the plane containing the lines…HardNumerical value
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.