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MHT CET202411 May 2024Evening 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 PQ is parallel to the plane x-4 y+3 z=1 is

Options

  1. A1 4
  2. B- 1 4
  3. C1 8
  4. D- 1 8

Correct answer

A. 1 4

Step-by-step solution

Let the position vector of Q be array ll & ( i - j +2 k )+ (-3 i + j +5 k ) & =(-3 +1) i +( -1) j +(5 +2) k & P Q =(-3 -2) i +( -3) j +(5 -4) k array Since PQ is parallel to the plane, aligned & (-3 -2)(1)+( -3)(-4)+(5 -4)(3)=0 & = 1 4 aligned

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