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MHT CET20243 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

Let (P(3,2,6) ) be a point in space and (Q ) be a point on the line ( r =( i - j +2 k )+ (-3 i + j +5 k ) ). Then the value of ( ) for which the vector (P Q ) is parallel to the plane (x-4 y+3 z=1 ) is:

Options

  1. A( 1 4 )
  2. B(- 1 4 )
  3. C( 1 8 )
  4. D(- 1 8 )

Correct answer

A. ( 1 4 )

Step-by-step solution

Any point on the vector ( r ) can be taken as, ( aligned & Q (1-3 ),( -1),(5 +2) gives & PQ = -3 -2, -3,5 -4 aligned ) Now, the ( PQ ) must be perpendicular to the normal for the given plane. ( aligned & 1(-3 -2)-4( -3)+3(5 -4)=0 & -3 -2-4 +12+15 -12=0 & 8 =2 & = 1 4 aligned )

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