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Manipal MET2011MathematicsThree Dimensional Geometry

The equation of plane passing through a point A(2,-1,3) and parallel to the vectors a =(3,0,-1) and b =(-3,2,2) is

Options

  1. A2 x-3 y+6 z+25=0
  2. B3 x-2 y+6 z+25=0
  3. C2 x-3 y+6 z-25=0
  4. D3 x-2 y+6 z-25=0

Correct answer

C. 2 x-3 y+6 z-25=0

Step-by-step solution

Since, plane is parallel to a given vector, it implies that normal of plane must perpendicular to the given vectors. Given point to which plane passes through is (2,-1,3) . Let A, B and C are direction ratios of its normal. Equation of plane is A(x-2)+B(y+1)+C(z-3)=0 Now, normal to plane A i +B j +C k is perpendicular to the given vectors and aligned & a =3 i +0 j - k & b =-3 i +2 j +2 k aligned 3 A+0 B-C=0 ..(i) and -3 A+2 B+2 C=0 ..(ii) From Eqs. (i) and (ii), we get A 2 = B -3 = C 6 Equation of plane be array ll

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