JEE Main 2018MathematicsThree Dimensional GeometryMediumMCQ

JEE Main 2018 — Three Dimensional Geometry Question with Solution

JEE Main 2018 (15 Apr)

Question

An angle between the plane x+y+z=5 and the line of intersection of the planes, 3x+4y+z-1=0 and 5x+8y+2z+14=0 is

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Show full solutionCorrect option: D
Correct answer
Dsin-1⁡317

Step-by-step explanation

Let n→ be the vector along the line of intersection of given planes.

⇒n→=i^j^k^341582=i^(0)−j^(6−5)+k^(24−20)=−j^+4k^

Now, angle between the plane x+y+z=5 and the line of intersection of the planes 3x+4y+z-1=0 and 5x+8y+2z+14=0 is equal to π2-cos-1⁡-1+43  17

=π2-cos-1⁡317

=sin-1⁡317 ∵sin-1x+cos-1x=π2

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About this question

This is a previous-year question from JEE Main 2018, 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.