JEE Main 2021MathematicsThree Dimensional GeometryHardMCQ

JEE Main 2021 — Three Dimensional Geometry Question with Solution

JEE Main 2021 (24 Feb Shift 2)

Question

The vector equation of the plane passing through the intersection of the planes r→·i^+j^+k^=1 and r→·i^-2j^=-2, and the point 1, 0, 2 is:

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Show full solutionCorrect option: A
Correct answer
Ar→·i^+7j^+3k^=7

Step-by-step explanation

r→·i^+j^+k^=1

r→·i^-2j^=-2

point 1, 0, 2

Eqn of plane

r→·i^+j^+k^-1+λ{r→·i^-2j^+2}=0

r→·{i^1+λ+j^1-2λ+k^1}-1+2λ=0

Point i^+0j^+2k^=r→

∴i^+2k^·{i^1+λ+j^1-2λ+k^1}-1+2λ=0

1+λ+2-1+2λ=0

λ=-23

∴r→·i^13+j^73+k^=73

r→·[i^+7j^+3k^]=7

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About this question

This is a previous-year question from JEE Main 2021, 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.