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MHT CET202313 May 2023Evening ShiftMathematicsThree Dimensional GeometryActual

A plane is parallel to two lines whose direction ratios are 2,0,-2 and -2,2,0 and it contains the point (2,2,2) . If it cuts co-ordinate axes at A , B , C then the volume of tetrahedron OABC (in cubic units) is

Options

  1. A216
  2. B6
  3. C36
  4. D9

Correct answer

C. 36

Step-by-step solution

The equation of plane passing through (2,2,2) is a (x-2)+ b (y-2)+ c ( z -2)=0 Also, 2 a -2 c =0-2 a+2 b=0 a = b = c aligned & x+y+z-6=0 & x 6 + y 6 + z 6 =1 aligned It cuts the co-ordinate axes at A (6,0,0) , B (0,6,0) and C (0,0,6) a =6 i , b =6 j , c =6 k Volume of tetrahedron = 1 6 [ array lll - a & b & c array ] aligned & = 1 6 | array lll 6 & 0 & 0 0 & 6 & 0 0 & 0 & 6 array | & =36 cubic units aligned

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