MHT CET 2017 Math Solved Paper

(d) It is given that, A(2, 3, 5), B (-1, 3, 2) and C( a, 5, u) are three vertices of ΔABC.
Let D be the mid-point of BC
So, coordinates of D = (

λ−1

2

,

5+3

2

,

µ+2

2

)
= (

λ−1

2

,4,

µ+2

2

)
So, direction ratios of
AD = (

λ−1

2

−2,4−3,

µ+2

2

−5)
= (

λ−5

2

,1,

µ−8

2

)

As, AD is equally inclined to both the coordinates axes.
Therefore, (

λ−5

2

=1=

µ−8

2

)
(

λ−5

2

=1) ⇒ λ = 7
And, (1=

µ−8

2

) ⇒ µ = 10