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AP EAMCET202421 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

If P (2, , ) lies on the plane x+2 y-z-2=0 an Q ( ,-1, ) lies on the plane 2 x-y+3 z+6=0 then 1 direction cosines of the line PQ are

Options

  1. A(- 4 17 , 0, 1 17 )
  2. B(+ 4 17 , 0, 1 17 )
  3. C( 1 17 , 0, 4 17 )
  4. D(- 1 17 , 0, 4 17 )

Correct answer

A. (- 4 17 , 0, 1 17 )

Step-by-step solution

aligned & P(2, , ) lies on x+2 y-z-2=0 & 2+2 - -2=0 & =2 ...(i) & Q( ,-1, ) lies on 2 x-y+3 z+6=0 & 2 +3 +7=0 aligned ...(ii) Solving (i) and (ii), =-2, =-1 PQ =-4 i + k So, direction cosines are ( -4 17 , 0, 1 17 )

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