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MHT CET202013 Oct 2020Morning ShiftMathematicsThree Dimensional GeometryActual

A plane E ₁ makes intercepts 1,-3,4 on the co-ordinate axes. The equation of a plane parallel to plane E ₁ and passing through (2,6,-8) is

Options

  1. Ax 2 - y 3 + z 4 +3=0
  2. Bx 1 - y 3 + z 4 +12=0
  3. Cx 1 - y 3 + z 4 +2=0
  4. Dx 3 - y 6 + z 2 + 13 3 =0

Correct answer

C. x 1 - y 3 + z 4 +2=0

Step-by-step solution

A plane E ₁ makes intercepts 1,-3,4 on the coordinate axes Equation of plane is x 1 + y -3 + z 4 =1 12 x-4 y+3 z=12 d.r.s. are 12,-4,3 Since required plane is parallel to given plane, normal vector n to required plane is n =12 i -4 j +3 k The vector equation of the plane passing through (2,6,-8) is r n = a n , where a =2 i +6 j -8 k a n =(12)(2)-(4)(6)+(3)(-8)=24-24-24=-24 Required equation is r (12 i -4 j +3 k )=-24 Cartesion form of equation is 12 x-4 y+3 z+24=0 x 1 - y 3 + z 4 +2=0

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