R divides the line joining two points P and Q whose position vectors are i +2 j - k and - i + j + k respectively in the ratio 2: 1 externally. S divides P Q internally in the ratio 2: 1 . Then, the position vector of the midpoint of the line joining R and S is

Step-by-step solution

We have, P= i +2 j - k and Q=- i + j + k R divides externally in the ratio 2: 1 R= ( i +2 j - k )-2(- i + j + k ) 1-2 R= i +2 j - k +2 i -2 j -2 k -1 =-3 i +3 k S divides internally in the ratio 2: 1 S= ( i +2 j - k )+2(- i + j + k ) 2+1 S= i +2 j - k -2 i +2 j +2 k 3 = - i +4 j + k 3 Mid-point of R and S , is -3 i +3 k + -I+4 j + k 3 2 = -9 i +9 k - i +4 j + k 6 = -10 i +4 j +10 k 6 = -5 3 i + 2 3 j + 5 3 k