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Manipal MET2015MathematicsThree Dimensional Geometry

The equation of the plane through the intersection of the planes x+y+z=1 and 2 x+3 y-z+4=0 and parallel to X -axis, is

Options

  1. Ay-3 z+6=0
  2. B3 y-z+6=0
  3. Cy+3 z+6=0
  4. D3 y-2 z+6 0

Correct answer

A. y-3 z+6=0

Step-by-step solution

The equation of the plane through the intersection of the planes x+y+z=1 and 2 x+3 y-z+4=0 is (x+y+z-1)+ (2 x+3 y-z+4)=0 or (2 +1) x+(3 +1) y+(1- ) z+4 -1=0 ...(i) It is parallel to X -axis. i.e. x 1 = y 0 = z 0 array ll & 1(2 +1)+0 (3 +1)+0(1- )=0 & =- 1 2 array On substituting =- 1 2 in Eq. (i), we get array r (2 x- 1 2 +1 ) x+ (3 -1 2 +1 ) y+ (1+ 1 2 ) z+4 (- 1 2 )-1=0 array aligned & -1 2 y+ 3 2 z-3 = & =0 & y-3 z+6 aligned =0 which is the equation of the required plane.

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