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=