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Manipal MET2016MathematicsThree Dimensional Geometry

The equation of the plane passing through the line of intersection of the planes x+y+z=6 and 2 x+3 y+4 z+5=0 and perpendicular to the plane 4 x+5 y-3 z=8 is

Options

  1. Ax+7 y+13 z-96=0
  2. Bx+7 y+13 z+96=0
  3. Cx+7 y-13 z-96=0
  4. Dx-7 y+13 z+96=0

Correct answer

B. x+7 y+13 z+96=0

Step-by-step solution

The intersection of two planes is aligned & (x+y+z-6)+ (2 x+3 y+4 z+5)=0 & (1+2 ) x+(1+3 ) y+(1+4 ) z+(-6+5 )=0 (i) aligned Since, this plane is perpendicular to the plane 4 x+5 y-3 z-8=0 (1+2 ) 4+(1+3 ) 5+(1+4 )(-3)=0 = -6 11 On putting the value of in Eq. (i), we get (- 1 11 ) x+ (- 7 11 ) y+ (- 13 11 ) z+ (- 96 11 )=0 x+7 y+13 z+96=0

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