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AP EAMCET2016MathematicsThree Dimensional Geometry

The cartesian equation of the plane whose vector equation is =(1+ - ) i +(2- ) j +(3-2 +2 ) k where , are scalars, is

Options

  1. A2 x+y=5
  2. B2 x-y=5
  3. C2 x-z=5
  4. D2 x+z=5

Correct answer

D. 2 x+z=5

Step-by-step solution

aligned & =(1+ - ) i +(2- ) j +(3-2 +2 ) k & = i + i - i +2 j - j +3 k -2 k +2 k & =( i +2 j +3 k )+ ( i - j -2 k )+ (- i +2 k ) aligned Equation of plane is given by r-( i +2 j +3 k ) +[( i - j -2 k ) (- i +2 k )]=0 array ll & r-( i +2 j +3 k ) (-2 i - k )=0 & r(2 i + k )-5=0 & r(2 i + k )=5 array Now, equation of plane in cartesian form aligned & (x i +y j +z k ) (2 j + k )=5 & 2 x+z=5 aligned

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