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

Question

The length of perpendicular from the origin to the plane \(\bar{r}\) = (3\(\hat{i}\) - 4\(\hat{j}\) - 12\(\hat{k}\)) + 39 = 0 is

A. 3 units 

B. 13/5 units 

C. 5/3 units 

D. None of these

Answer 1

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

Formula Used: Equation of a plane is \(\hat{u}\) . \(\bar{r}\) = p where is the unit vector normal to the plane, \(\bar{r}\) represents a point on the plane and p is the distance of the plane from the origin. 

Explanation:

Therefore, length of perpendicular from origin to plane is 3 units.