MHT CET 2019 Math Solved Paper

let the co-ordinates of foot of perpendicular from the origin (0) to the plane 2x−y+5z−3=0 is P(a, b,c).
∴ direction ratios of OP are < a, b, c > which is also the direction ratios of normal to the given plane. ∴

a

2

=

b

−1

=

c

5

=k
⇒a=2k,b=−k,c=5k
∵ P(a, b, c) passes the given plane
∴2(2k)−(−k)+5(5k)=3
⇒4k+k+25k=3
⇒k=

3

30

=

1

10