BITSAT 2012 Paper

We know that the length of the perpendicular from the point (x1,y1,z1) to the plane ax + by + cz + d = 0 is

|ax1+by1+cz1+d|

√a2+b2+c2

and the co-ordinate (α, β, γ) of the foot of the ⊥ are given by

α−x1

a

=

β−y1

b

=

γ−z1

c

= - (

ax1+by1+cz1+d

a2+b2+c2

) ... (1)
In the given ques, x1 = 7, y1 = 14, z1 = 5,
a = 2 b = 4,c = -1, d = -2
By putting these values in (1), we get
α7*2 =

β−14

4

=

γ−5

−1

= -

63

21

⇒ α = 1 , β = 2 and γ = 8