The two vector i + j + k and i +3 j +5 k represent the two sides A B and A C respectively of a A B C . The length of the median through A is

Step-by-step solution

We know that, the sum of three vectors of triangle is zero. array ll & A B + B C + C A =0 & B C = A C - A B B M = & A C - A B 2 ( since, M is a mid-point of B C) array And also, A B + B M + M A =0 A B + A C - A B 2 = A M A M = A B + A C 2 A M = ( i + j + k )+( i +3 j +5 k ) 2 A M = 2 i +4 j +6 k 2 A M = i +2 j +3 k | A M |= (1)²+(2)²+(3)² = 1+4+9 = 14