Let P (4, 3, -1) and Q (6, -1, 3) be two points in three- dimensional space, find the distance between P and Q, Also find an equation for the sphere w

Question

Let P (4, 3, -1) and Q (6, -1, 3) be two points in three- dimensional space, find the distance between P and
Q, Also find an equation for the sphere whose center is P and for which the segment is a radius of the
sphere.

Answer 1

Distance formula :

 

d = √[(x₂-x₁)²  + (y₂-y₁)² + (z₂-z₁)² ]

 

P(4,3,-1)
Q(6,-1,3)

 

d = √[(6-4)²  + (-1-3)² + (3--1)² ]

d = √[(4 + 16 + 16 ]

d = √[(36]

d = 6

 

General equation for a sphere whose center is (a,b,c) and radius is r :

 

(x-a)² +(y-b)² +(z-c)² =r²  

 

(x-4)²+(y-3)²+ (z+1)² = 36