ABC is a triangle in a plane with vertices A (2,3,5), B (-1,3,2) and C ( , 5, ) . If median through A is equally inclined to the co-ordinate axes, then value of + is

Step-by-step solution

Let AD be the median Co-ordinates of aligned & D ( x₁+x₂ 2 , y₁+y₂ 2 , z ₁+ z ₂ 2 ) & D ( -1 2 , 4, +2 2 ) & AD = ( -1 2 -2 ) i +(4-3) j + ( +2 2 -5 ) k & AD = ( -5 2 ) i + j + ( -8 2 ) k aligned Since AD makes equal angle with co-ordinate axes, the direction ratios are equal. -5 2 =1= -8 2 Consider, aligned & -5 2 =1 & -5=2 aligned aligned & =7 & and -8 2 =1 & -8=2 & =10 & + =7+10=17 & aligned