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

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 in normal to the oiven plane, therefore equation of P Q is r =( i + ) + ( 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 ) i.e., (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 & = ( +2 2 ) i + 2 j + ( 6+ 2 ) k & = ( 2 +1 ) i + 2 j + (