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MHT CET202416 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

A plane makes positive intercepts of unit length on each of X and Y axis. If it passes through the point (-1,1,2) and makes angle with the X -axis, then is

Options

  1. A⁻¹ ( 2 3 )
  2. B⁻¹ ( 1 3 )
  3. C⁻¹ ( 1 3 )
  4. D⁻¹ ( 2 3 )

Correct answer

D. ⁻¹ ( 2 3 )

Step-by-step solution

Equation of plane in intercept form is x a + y b + z c =1 Here, a =1, ~b =1 x 1 + y 1 + z c =1 Since this plane passes through the point (-1,1,2) aligned & -1+1+ 2 c =1 & c=2 aligned Equation of plane is aligned & x+y+ z 2 =1 & 2 x+2 y+z=2 aligned D.r.s of X -axis are 1,0,0 . aligned & = 2(1)+0+0 4+4+1 1 & = 2 3 & = ⁻¹ ( 2 3 ) aligned

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