BITSAT 2012 Paper

The direction ratios of the line are 3 – 2, – 4 – (–3), – 5 –1 i.e. 1, –1, – 6
Hence equation of the line joining the given points is

x−2

1

=

y+3

−1

=

z−1

−6

= r (say)
Coordinates of any point on this line are (r + 2, – r – 3, – 6r + 1)
If this point lies on the given plane 2x + y + z = 7,
then 2(r + 2) + (– r – 3) + (– 6r + 1) = 7 ⇒ r = – 1
Coordinates of any point on this line are
(– 1 + 2, – (– 1) – 3, – 6 (–1) + 1) i.e. (1, – 2, 7)