The equation of the plane passing through the points (2, -1, 0), (3, -4, 5) and parallel to the line 2x = 3y = 4z is :

29x – 27y – 22z = 85

Give line is 2x = 3y = 4z

i.e.,  $\frac{x}{6}=\frac{y}{4}=\frac{z}{3}$

Let the plane be

Ax + by + cz = 1

We have

6a + 4b + 3c = 0

2a – b = 1

3a – 4b + 5c = 1

$\Rightarrow a=\frac{29}{85}, b=\frac{27}{85}, c=-\frac{22}{85}$

Thus equation of plane is

29x – 27y – 22z = 85