Question

If d is the shortest distance of the point (1, 2, −1) from the surface x² + y² + z² = 54, then d/√6 is equal to ______.

Answer 1

See Fig. 

The equation

x² + y² + z² = 54

is a sphere with centre (0, 0, 0) and radius = √54 = 3√6. P(1, 2, −1) is a point inside the sphere such that

Thus distance of P from the surface of the sphere is 

d = 3√6 - √6 = 2√6

Therefore