JEE Main 2020MathematicsThree Dimensional GeometryMediumNumerical

JEE Main 2020 — Three Dimensional Geometry Question with Solution

JEE Main 2020 (03 Sep Shift 2)

Question

Let a plane P contain two lines r→=i^+λi^+j^, λ∈R and r→=-j^+μj^-k^, μ∈R. If Qα, β, γ is the foot of the perpendicular drawn from the point M1, 0, 1 to P, then 3α+β+γ equals .......

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Show full solutionCorrect answer: 5
Correct answer
5

Step-by-step explanation

Normal vector to the plane containing to given lines n→=i^j^k^11001-1=-i^+j^+k^

Direction ratios of normal vector =-1, 1, 1.

Equation of plane will be -1x-1+1y-0+1z-0=0

⇒ x-y-z-1=0

If x, y, z is foot of perpendicular drawn from M1, 0, 1 on the plane, then

⇒x-11=y-0-1=z-1-1=-1-0-1-13

⇒x=43, y=-13, z=23

⇒α+β+γ=43-13+23=53

⇒3α+β+γ=5.

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About this question

This is a previous-year question from JEE Main 2020, 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.