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JEE Advanced2009MathematicsThree 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. A1 / 4
  2. B-1 / 4
  3. C1 / 8
  4. D-1 / 8

Correct answer

A. 1 / 4

Step-by-step solution

O Q =(1-3 ) i +( -1) j +(5 +2) k and O P =3 i +2 j +6 k , where O is origin. aligned & Now, P Q =(1-3 -3) i +( -1-2) j & +(5 +2-6) k & =(2-3 ) i +( -3) j +(5 -4) k & aligned P Q is parallel to the plane array rr & x-4 y+3 z=1 . & -2-3 -4 +12+15 -12=0 & 8 =2 = 1 4 array

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