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

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