Question

Find the length of perpendicular drawn from the origin to the plane 2x – 3y + 6z + 21 = 0.

Answer 1

Given : 

Equation of plane : 2x – 3y + 6z + 21 = 0 

To Find : 

Length of perpendicular drawn from origin to the plane = d 

Formulae : 

1) Distance of the plane from the origin : 

Distance of the plane from the origin is given by,

d = \(\frac{p}{|\bar{n}|}\)

Answer : 

For the given equation of plane 

2x – 3y + 6z = -21 

Direction ratios of normal vector are (2, -3, 6) 

Therefore, equation of normal vector is

From given equation of plane, 

p = -21 

Now, distance of the plane from the origin is