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Manipal MET2014MathematicsThree Dimensional Geometry

The image of the point with position vector i +3 k in the plane r ( i + j + k )=1 is

Options

  1. Ai +2 j + k
  2. Bi -2 j + k
  3. C- i -2 j + k
  4. Di +2 j - k

Correct answer

C. - i -2 j + k

Step-by-step solution

Let Q be the image of the point P( i +3 k ) in the plane r ( i + j + k )=1 . Then P Q is normal to the plane. Since P Q passes through P and is normal to the given plane, therefore equation of P Q is r =( i +3 k )+ ( i + j + k ) Since, Q lies on the line P Q , so, let the position vector of Q be ( i +3 k )+ ( i + j + k ) (1+ ) i + j +(3+ ) k Since R is the mid point of P Q , therefore position vector of R is aligned & (1+ ) i + j +(3+ ) k + i +3 k 2 & or ( +2 2 ) i + ( 2 ) j + (3+ 2 ) k & or ( 2 +1 ) i + ( 2 ) j +

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