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AP EAMCET202123 Aug 2021Evening ShiftMathematicsThree Dimensional GeometryActual

The plane passing through (2,1,-3) and perpendicular to 3 i - j +2 k contains the points

Options

  1. A(1,5,1) and (3,0,-5)
  2. B( 1 3 , 3, 1 2 ) and (1,5, 1 2 )
  3. C(3,1,-5) and ( 1 3 , 3, 1 2 )
  4. D(1,5,3) and (3,0,1)

Correct answer

B. ( 1 3 , 3, 1 2 ) and (1,5, 1 2 )

Step-by-step solution

Since, we know that the equation of plane passing through a point A and perpendicular to vector n is ( r - a ) n =0 where, a is the position vector of point and n is the normal vector. Given, A=(2,1-3), n =3 i - j +2 k array ll & a =2 i + j -3 k and & r =x i +y j +z k array ( r a ) n =0 aligned & (x-2) i +(y-1) j +(z+3) k 3 i - j +2 k =0 & 3(x-2)-(y-1)+2(z+3)=0 & 3 x-6-y+1+2 z+6=0 aligned 3 x-y+2 z+1=0 ( 1 3 , 3, 1 2 ) and (1,5, 1 2 ) satisfies the above equation.

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