JEE Main 2019MathematicsThree Dimensional GeometryMediumMCQ

JEE Main 2019 — Three Dimensional Geometry Question with Solution

JEE Main 2019 (10 Apr Shift 1)

Question

If the length of the perpendicular from the point β,0,β,β≠0 to the line, x1=y-10=z+1-1 is 32 , then β is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B-1

Step-by-step explanation

Let Q=λ,1,-λ-1

Direction ratio's of PQ≡λ-β,1-0, -λ-1-β

∴PQ is perpendicular to given line, hence

1λ-β+01-1-λ-1-β=0

⇒λ-β+λ+1+β=0

⇒λ=-12

∴  PQ= λ-β2+12+-λ-1-β2=32 

⇒-12-β2+12+12-1-β2=32

⇒β2+14+β+1+β2+14+β=32

⇒2β2+2β=0⇒β=0  or -1

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About this question

This is a previous-year question from JEE Main 2019, 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.