JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 13 April 2023, Shift 1, Maths Q17

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

The distance of the point

(-1,2,3)

from the plane

\vec{r}\cdot\left(\hat{i}-2\hat{j}+3\hat{k}\right)=10

parallel to the line of the shortest distance between the lines

\vec{r}=\left(\hat{i}-\hat{j}\right)+\lambda\left(2\hat{i}+\hat{k}\right)

and

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

(1) $3\sqrt{5}$
(2) $2\sqrt{6}$ Official answer
(3) $3\sqrt{6}$
(4) $2\sqrt{5}$

Official answer

Option 2

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Point-Plane Distance
Idea tested: Distance Along a Line

Same idea in other shifts

Asked 9× in all

4 Apr 2026, Shift 1 · Q15The square of the distance of the point $(-2,-8,6)$ from the line $\frac{x-1}{1}=\frac{y-1}{2}=\frac{z}{-1}$ along the line…MediumSingle correct
11 Apr 2023, Shift 2 · Q16Let the line passing through the points $P(2, -1, 2)$ and $Q(5, 3, 4)$ meet the plane $x - y + z = 4$ at the point $R$ . Then the distance…HardSingle correct
15 Apr 2023, Shift 1 · Q29Let the plane P contain the line $2x+y-z-3=0=5x-3y+4z+9$ and be parallel to the line $\frac{x+2}{2}=\frac{3-y}{-4}=\frac{z-7}{5}$ . Then…HardNumerical value
29 Jul 2022, Shift 1 · Q9If the foot of the perpendicular from the point $A(-1, 4, 3)$ on the plane $P : 2x + my + nz = 4$ , is…MediumSingle correct
30 Jun 2022, Shift 1 · Q16The distance of the point $(3, 2, -1)$ from the plane $3x - y + 4z + 1 = 0$ along the line $\frac{2-x}{2} = \frac{y-3}{2} = \frac{z+1}{1}$ …MediumSingle correct
27 Aug 2021, Shift 1 · Q73The distance of the point $(1, -2, 3)$ from the plane $x-y+z=5$ measured parallel to a line, whose direction ratios are $2, 3, -6$ is :MediumSingle correct
16 Mar 2021, Shift 2 · Q83If the distance of the point (1, $-2$ , 3) from the plane $x+2y-3z+10=0$ measured parallel to the line,…MediumNumerical value
4 Sep 2020, Shift 2 · Q67The distance of the point $(1, -2, 3)$ from the plane $x-y+z=5$ measured parallel to the line $\frac{x}{2}=\frac{y}{3}=\frac{z}{-6}$ 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.