JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 11 April 2023, Shift 2, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

Let the line

l : x = \frac{1-y}{-2} = \frac{z-3}{\lambda}

\lambda \in \mathbb{R}

meet the plane

P : x + 2y + 3z = 4

at the point

(\alpha, \beta, \gamma)

. If the angle between the line

l

and the plane

P

\cos^{-1}\left(\sqrt{\frac{5}{14}}\right)

, then

\alpha + 2\beta + 6\gamma

is equal to ________.

Official answer

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Angle Between Lines
Idea tested: Angle: Line and Plane

Same topic in other shifts

All Angle Between Lines questions

6 Apr 2026, Shift 1 · Q16Let a line L be perpendicular to both the lines $\mathrm{L}_1:\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}$ and…MediumSingle correct
26 Jun 2022, Shift 1 · Q14If the two lines $l_1 : \frac{x-2}{3} = \frac{y+1}{-2}, z = 2$ and $l_2 : \frac{x-1}{1} = \frac{2y+3}{\alpha} = \frac{z+5}{2}$ are…MediumSingle correct
27 Jun 2022, Shift 1 · Q14If two straight lines whose direction cosines are given by the relations $l+m-n=0$ , $3l^2+m^2+cnl=0$ are parallel, then the positive value…MediumSingle correct
3 Aug 2021, Shift 2 · Q76Let $L_1$ and $L_2$ be two lines passing through the points $P(b-c, c-a, a-b)$ and $Q\left(\frac{1}{l}, \frac{1}{m}, \frac{1}{n}\right)$ …HardSingle correct
4 Aug 2021, Shift 1 · Q87Maximum number of lines, through the origin which make equal angles with the three coordinate axes in XYZ-space, is ________.EasyNumerical value
26 Aug 2021, Shift 2 · Q70A hall has a square floor of dimension $10\ \mathrm{m}\times10\ \mathrm{m}$ (see the figure) and vertical walls. If the angle GPH between…MediumSingle correctHas a figure

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.