`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`

Options

A. 10,7
B. 9, 10
C. 7,9
D. 7,10

Answer

D

Explanation

Given, A(2,3,5),B(-1,3,2) and C`(lamda,5,mu)` be the vertices of `DeltaABC`.
Let D be the median through A to BC
`=((lamda-1)/(2),(5+3)/(2),(mu+2)/(2))`
`=((lamda-1)/(2),(8)/(2),(mu+2)/(2))`
`z-=((lamda-1)/(2),4,(mu+2)/(2))`
Now, direction ratios of
`AD=((lamda-1)/(2)-2,4-3,(mu+2)/(2)-5)`

i.e., `((lamda-1-4)/(2),1,(mu-2-10)/(2))`
i.e., `((lamda-5)/(2),1,(mu-8)/(2))`
Since the line AD is equally inclined to the coordinates axes.
`therefore(lamda-5)/(2)=1=(mu-8)/(2)`
On solving first two, we get
`(lamda-5)/(2)=1`
`implieslamda=7`
On solving last two, we get
`1=(mu-8)/(2)`
`impliesmu=10`