Sol. The required line passing through the point P(2, 1, 1) in the plane 2x + y –5z = 0 and is having greatest

slope, so it must be perpendicular to the line of

intersection of the planes

2x + y –5z = 0 … (i)

and 4x –3y +7z = 0 … (ii)

Let the d.r'.s of the line of intersection of (i) and (ii) are a, b, c

⇒ 2a + b –5c = 0 and 4a –3b + 7c = 0

{as dr'.s of straight line (a, b, c) is perpendicular to d.r'.s of normal to both the planes}

⇒ = =

Now let the direction ratio of required line be

proportional to l, m, n then its equation be =

= where 2 λ + m –5n = 0 and 4 λ + 17m + 5n = 0

So, = =

Thus the required line is = =