Mark against the correct answer in each of the following:
A plane cuts off intercepts 3, -4, 6 on the coordinate axes. The length of perpendicular from the origin to this plane is
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