JEE Main 2023MathematicsThree Dimensional GeometryMediumMCQ

JEE Main 2023 — Three Dimensional Geometry Question with Solution

JEE Main 2023 (30 Jan Shift 2)

Question

A vector v→ in the first octant is inclined to the x axis at 60°, to the y-axis at 45° and to the z-axis at an acute angle. If a plane passing through the points 2,-1,1 and a,b,c, is normal to v→, then

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Show full solutionCorrect option: C
Correct answer
Ca+2b+c=1

Step-by-step explanation

Direction cosines l,m and n of given vector v→,

l=cos60∘=12

m=cos45∘=12

n=cosγ

v→=cos60°i^+cos45°j^+cosγk^....(1)

We know,

l2+m2+n2=1

⇒14+12+cos2γ=1  (γ→Acute)

⇒cosγ=12

⇒ γ=60°

Equation of plane is 12x-2+12y+1+12z-1=0

⇒x2+y2+z2=12

⇒  x+2y+z=1

a,b,c lies on it,

⇒  a+2b+c=1

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About this question

This is a previous-year question from JEE Main 2023, 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.