Question

A sphere has center (0, 0, 0) and radius 5.
Tell whether each of the following points is inside, outside, or on the sphere.
a. A(0, -3, 4)
b. B(1, -1,-1)
c. C(4, -6, -10)

Answer 1

which equation would i need to use

Answer 2

what are x,y,z

Answer 3

For this problem you need to calculate the distance from the origin for each point. If it is less or more than 5

Answer 4

Do you know how to do that for a 3 dimensional space?

Answer 5

His method was over-complicated.

Answer 6

um not a clue how to do that

Answer 7

So here is the general formula for the distance between 2 point P(p1,p2,p3) and Q(q1,q2,q3) in 3D:

Answer 8

\[d(p,q)=\sqrt{(p _{1}-q _{1})^2+(p _{2}-q _{2})2+(p _{3}-q _{3})^2}\]

Answer 9

Here luckily P is (0,0,0)

Answer 10

Q will be the 3 points given.
When you put these in you will get a number, If it is =5 it is on the sphere, less than 5 inside, more than 5 outside.
Hope this helped

Answer 11

I will do B for you as that is the easiest:
distance d(0,B)=\[\sqrt{(0-1)^2+(0-(-1))^2+(0-(-1))^2}=\sqrt{3}\]

Answer 12

So it is inside the sphere

Answer 13

A will be on the sphere, C will be outside. But you will have to do the calculation :)

Answer 14

yes thanks for explaining