Given: Plane makes intercepts 3, -4 and 6 with the coordinate axes.

Formula Used: Equation of plane is where (x, y, z) is a point on the plane and a, b, c are intercepts on x-axis, y-axis and z-axis respectively.

Normal Form of a plane ⇒ lx + my + nz = p where (l, m, n) is the direction cosines and p is the distance of perpendicular to the plane from the origin.

Explanation:

Equation of the given plane is

i.e., 4x – 3y + 2z = 12 … (1)

which is of the form ax + by + cz = d

Direction ratios are (4, -3, 12)

So,

= √29

Dividing (1) by 13,

which is in the normal form

Therefore length of perpendicular from the origin is units