Let A (2,3,5), B (-1,3,2) and C ( , 5, ) be the vertices of a ABC . If the median through A is equally inclined to the coordinate axes, then:

Step-by-step solution

If D be the mid-point of B C , then D= ( -1 2 , 4, +2 2 ) Direction ratios of AD are -5 2 , 1, -8 2 Since median AD is equally inclined with coordinate axes, therefore direction ratios of AD will be equal, i.e, aligned & ( -5 2 )^2 ( -5 2 )^2+1+ ( -8 2 )^2 &= 1 ( -5 2 )^2+1+ ( -8 2 )^2 &= ( -8 2 )^2 ( -5 2 )^2+1+ ( -8 2 )^2 & ( -5 2 )^2=1= ( -8 2 )^2 aligned aligned & ( -5 2 )^2=1= ( -8 2 )^2 & =7,3 and =10,6 aligned If =7 and =10 Then = 7 10 10 -7 =0