Finding points on a line in 3d

[Mosier]

Homework Statement

It's been a while since I've done this stuff D:

So Given Points A(a,1,0), B(1,b,0) and C(1,0,c) with |AC|=|BC|=|AB|

Find the points algebraically

Homework Equations

Unfortunately, i don't have much knowledge on this. I am sure there's a 3d point slope style formula around somewhere though :s

The Attempt at a Solution

At first my guess was to try making it a vector such that SQRT((Xc-Xa)^2+(Yc-Ya)^2+(Zc-Za)^2) and so on, but from there i was confused on how to find the points.

I appreciate the potential help, thanks guys :D

 

[icystrike]

Homework Statement

It's been a while since I've done this stuff D:

So Given Points A(a,1,0), B(1,b,0) and C(1,0,c) with |AC|=|BC|=|AB|

Find the points algebraically

Homework Equations

Unfortunately, i don't have much knowledge on this. I am sure there's a 3d point slope style formula around somewhere though :s

The Attempt at a Solution

At first my guess was to try making it a vector such that SQRT((Xc-Xa)^2+(Yc-Ya)^2+(Zc-Za)^2) and so on, but from there i was confused on how to find the points.

I appreciate the potential help, thanks guys :D

Is there a need for X,Y and Z to be in the square?

 

[Mark44]

Homework Statement

It's been a while since I've done this stuff D:

So Given Points A(a,1,0), B(1,b,0) and C(1,0,c) with |AC|=|BC|=|AB|

Find the points algebraically

Homework Equations

Unfortunately, i don't have much knowledge on this. I am sure there's a 3d point slope style formula around somewhere though :s

The Attempt at a Solution

At first my guess was to try making it a vector such that SQRT((Xc-Xa)^2+(Yc-Ya)^2+(Zc-Za)^2) and so on, but from there i was confused on how to find the points.

I appreciate the potential help, thanks guys :D

Write the vector that represents the vector AB. Write an expression that represents its length. For example, AB = (1 - a, b - 1, 0). |AB| = sqrt((1 - a)^2 + (b - 1)^2).
Do the same with vector BC. Write an expression that represents its length.
Do the same with vector AC. Write an expression that represents its length.

You are given that |AB| = |BC|, |BC| = |AC|, and |AB| = |BC|. Substitute the expressions you already found in these three equations.