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AP EAMCET201920 Apr 2019Morning ShiftMathematicsThree Dimensional GeometryActual

The equation of the plane passing through the point ( i +2 j - k ) and perpendicular to the line of intersection of the planes ( r (3 i - j + k )=1 ) and ( r ( i +4 j -2 k )=2 ), is

Options

  1. A( r (-2 i -5 j + k )=0 )
  2. B( r ( i +7 j +4 k )=0 )
  3. C( r (2 i -7 j -13 k )=1 )
  4. D( r (-2 i +7 j +13 k )=0 )

Correct answer

C. ( r (2 i -7 j -13 k )=1 )

Step-by-step solution

Equation of plane passes through the point (( i +2 j - k )=(1,2,-1) ) having direction ratios to normal are (a, b, c ) is (a(x-1)+b(y-2)+c(z+1)=0 ) ( ) Plane (i) is perpendicular to line of intersection of planes ( r (3 i - j + k )=1 ) and ( r ( i +4 j -2 k )=2 ) ( ) (3 a-b+c=0 ) and (a+4 b-2 c=0 ) ( aligned & a 2-4 = -b -6-1 = c 12+1 & a 2 = b -7 = c -13 aligned ) So, equation of required plane is ( array cc & 2(x-1)-7(y-2)-13(z+1)=0 & 2 x-7 y-13 z-2+14-13=0 & 2 x-7 y-13 z=1 or & r (2 i -7 j -13 k )=1 array ) Henc

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