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AP EAMCET201923 Apr 2019Morning ShiftMathematicsThree Dimensional GeometryActual

The direction cosines of the normal drawn to the plane passing through the points ((2,-1,5),(1,-3,4),(5,2,1) ) are

Options

  1. A( 11 179 , -7 179 , 3 179 )
  2. B( 9 134 , -7 134 , 2 134 )
  3. C( 11 179 , 7 179 , -3 179 )
  4. D( 9 134 , 7 134 , -2 134 )

Correct answer

A. ( 11 179 , -7 179 , 3 179 )

Step-by-step solution

Let (A=(2,-1,5) ) and (C=(5,2,1) ) ( ) Equation of plane passing through (A, B, C ) is ( aligned & | array ccc x-x₁ & y-y₁ & z-z₁ x₂-x₁ & y₂-y₁ & z₂-z₁ x₃-x₁ & y₃-y₁ & z₃-z₁ array |=0 & | array ccc x-2 & y+1 & z-5 -1 & -2 & -1 3 & 3 & -4 array |=0 & 11 x-7 y+3 z-26=0 aligned ) Required dc's are ( aligned & = 11 121+49+9 , -7 121+49+9 , 3 121+49+9 & = ( 11 179 , -7 179 , 3 179 ) aligned ) ( ) Hence, answer is (a).

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