JEE Main 2022MathematicsThree Dimensional GeometryEasyMCQ

JEE Main 2022 — Three Dimensional Geometry Question with Solution

JEE Main 2022 (24 Jun Shift 2)

Question

Let the points on the plane P be equidistant from the points -4,2,1 and 2,-2,3. Then the acute angle between the plane P and the plane 2x+y+3z=1 is

Choose an option

Show full solutionCorrect option: C
Correct answer
Cπ3

Step-by-step explanation

Plotting the diagram of the given information we get,

Normal vector of plane will be =AB→=OB→-OA→

=6i^-4j^+2k^ =23i^-2j^+k^

Now equation of plane is given by,

P≡3x+1-2y+1z-2=0

P≡3x-2y+z+1=0

Assuming other plane to be P'≡2x+y+3z-1=0

Now the angle between them is given by, cosθ=n^1·n^2n1n2

θ=cos-16-2+314×14

θ=cos-1714==cos-112=π3

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Three Dimensional Geometry chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2022, covering the Three Dimensional Geometry chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.