Geometry problem

[Merida]

Question and figure in diagram
I don’t know how to start off

 

[skeeter]

I'd start with letting D be located at the origin, DA be the positive x-axis, DC be the positive y-axis, and DP be the positive z-axis.

Label coordinates for points D, P, C, A, and B

let (x,y,z) be the sphere center which is equidistant from points P, B, C, and D

 

[Deleted member 4993]

Question and figure in diagram. I don’t know how to start off

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING

Please share your work/thoughts about these problems.

 

[Merida]

I'd start with letting D be located at the origin, DA be the positive x-axis, DC be the positive y-axis, and DP be the positive z-axis.

Label coordinates for points D, P, C, A, and B

let (x,y,z) be the sphere center which is equidistant from points P, B, C, and D

Yeah thanks got it

 

[Merida]

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING

Please share your work/thoughts about these problems.
View attachment 22880

Ok so I got centre as ( 1 , 0 , 1 ) . How to find the radius and in turn the volume now

 

[skeeter]

If B = (1,1,0), then C = (0,2,0)

Looks like you have the x and y axes switched

The center I calculated is different from yours

 

[Merida]

Ok then , the centre comes out as ( 0 , 1 ,1 ) . But how can one decide which axis is to be taken as the x axis and which one as the y-axis

If B = (1,1,0), then C = (0,2,0)

Looks like you have the x and y axes switched

The center I calculated is different from yours

 

[skeeter]

you make the decision ... just make sure the coordinates of all your labeled points match up correctly with that decision