`A B C` is a triangle and `A=(235)dotB=(-1,3,2)a n dC=(lambda,5,mu)dot` If the median through `A` is equally inclined to the axes, then find the value of `lambdaa n dmudot`

Explanation

Midpoint of BC is `((lamda-1)/(2),4, (2+mu)/(2))`
Direction ratios of the median through A are
`" "(lamda-1)/(2)-2, 4-3 and (2+mu)/(2)-5, i.e., (lamda-5)/(2), 1 and (mu-8)/(2).`
The median is equally inclined to the axes, so the direction ratios must be equal. Therefore,
`" "(lamda-5)/(2)=1=(mu-8)/(2)rArrlamda=7, mu=10`