Find the length of the perpendicular from the origin to the plane r.(3i - 12j - 4k) + 39 = 0

Question

Find the length of the perpendicular from the origin to the plane \(\bar{r}\).(3\(\hat{i}\) - 12\(\hat{j}\) - 4\(\hat{k}\)) + 39 = 0 Also write the unit normal vector from the origin to the plane.

Answer 1

Given : 

Equation of plane : \(\bar{r}\).(3\(\hat{i}\) - 12\(\hat{j}\) - 4\(\hat{k}\)) + 39 = 0

To Find : 

i) Length of perpendicular = d 

ii) Unit normal vector = \(\hat{n}\)

Formulae : 

1) Unit Vector :

2) Length of perpendicular : 

The length of the perpendicular from the origin to the plane 

\(\bar{r}.\bar{n}\) = p is given by,

The length of the perpendicular from the origin to the given plane is