BITSAT 2019 Slot 2 Solved Paper

Given line

x−1

−1

=

y−2

3

=

z−4

1

is passes through P(1,2,4)
To find the reflection of line we need one more point on the line clearly M(0,5,5) also lie on line. Let N(α,β,γ) be the reflection M in the
x+y+z=7
∴

α

2

+

β+5

2

+

γ+5

2

+7
⇒α+β+γ=4
Also, MN is perpendicular, i.e. parallel to the normal of the plane
∴

α

1

=

β−5

1

=

γ−5

1

=λ
⇒α=λ,β=λ+5,γ=λ−5
∴λ+λ+5+λ+5=4
⇒λ=−2
∴N=(−2,3,5)
Equation PN is

x−1

−3

=

y−2

1

=

z−4

−1