Question

Find the Maximum and minimum distance of the point (1, 2, 3) from the sphere x²+y²+z²=1

Answer 1

1231231231202.

6216

30

.3

2

320

3265+20

306+25

320.326+2

0

Answer 2

Answer:

Min distance = 2.74

Max Distance = 4.74

Step-by-step explanation:

The center of sphere x^2 + y^2 + z^2 = 1 is at (0,0,0)

Radius = 1 unit.  

Minimum distance from  point (1,2,3) on the facing side of the sphere.  

Maximum distance is on exactly opposite side of the sphere. This line goes through center of sphere.

From the diagram attached, AP is minimum distance, BP is maximum distance.  

Minimum distance AP = Distance between OP – radius.  

= √(1² + 2² + 3²) – 1 = √(14) – 1 = 3.74 – 1 = 2.74.  

Maximum distance BP = Distance between OP + radius

= √(1² + 2² + 3²) + 1 = √(14) + 1 = 3.74 + 1 = 4.74.