Find the shortest distance, d, from the point (5, 0, −6) to the plane x + y + z = 6.

Step-by-step explanation:

The shortest distance d, of a point (a, b, c) from a plane mx + ny + tz = r is given by:

                  --------------------(i)

From the question,

the point is (5, 0, -6)

the plane is x + y + z = 6

Therefore,

a = 5

b = 0

c = -6

m = 1

n = 1

t = 1

r = 6

Substitute these values into equation (i) as follows;

Therefore, the shortest distance from the point to the plane is