BITSAT 2017 Slot 2 Solved Paper

Given equation of plane is x+y+z=5.
The distance measured along the line x=y=z.
Direction ratios of the given line is (1,1,1).
So, the equation of line PQ is

x−1

1

=

y+5

1

=

z−9

1

=λ
⇒x=λ+1,y=λ−5,z=λ+9
lies on the plane x+y+z=5
∴(λ+1)−(−λ+5)+(λ+9)=5
⇒λ=−10
The coordinate of Q is (−9,−15,−1) and the coordinate of P is (1,−5,9)
PQ=√(10)2+(10)2+(10)2=10√3
∴2√3k=10√3⇒k=5