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MHT CET202120 Sep 2021Evening ShiftMathematicsThree Dimensional GeometryActual

The Cartesian equation of the plane r =( i - j )+ ( i + j + k )+ ( i -2 j +3 k ) is

Options

  1. Ax + y + z =0
  2. B5 x +2 y +3 z =0
  3. C2 x+y+z=0
  4. D5 x -2 y -3 z -7=0

Correct answer

D. 5 x -2 y -3 z -7=0

Step-by-step solution

aligned & r =( i - j )+ ( i + j + k )+ ( i -2 j +3 k ) & a = i - j , A = i + j + k , B = i -2 j +3 k aligned n is er A and B aligned & n = A B = | array ccc i & j & k 1 & 1 & 1 1 & -2 & 3 array | & = i (3+2)- j (3-1)+ k (-2-1)=5 i -2 j -3 k & a n = d =( i - j ) (5 i -2 j -3 k )=5+2=7 & r (5 i -2 j -3 k )=7 & Cartesian equation is 5 x -2 y -3 z -7=0 aligned

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