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Question: Answered & Verified by Expert
Which one of the following planes is normal to the plane $3 x+y+z=5 ? \quad$
MathematicsThree Dimensional GeometryNDANDA 2008 (Phase 2)
Options:
  • A $x+2 y+z-6$
  • B $x-2 y+z-6$
  • C $x+2 y-z=6$
  • D $x-2 y-z=6$
Solution:
2038 Upvotes Verified Answer
The correct answer is: $x-2 y-z=6$
Direction cosines of the normal to the plane $3 x+y+z=5$ are $3,1,1$
Direction cosines of the normal to the plane $x-2 y-z=6$ are $1,-2,-1$
Sum of the product of direction cosines $=3 \times 1+1 \times(-2)+1 \times(-1)=0$
Hence, normals to the two planes are perpendicular to each other. Therefore two planes are alsoperpendicular.

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