3D Linear equation problem

[mScientist]

Hi,

I have two points in 3D space:

 

point A: (1,2,3)

point B: (4,7,6)

 

I want to find a third point between the two, where z = 5

 

So,

point C: (x,y,5)

 

How can I calculate x and y for point C.

 

Thanks.

[Shadow]

Hint: The point C lies on the line passing through A and B. How would one go about writing down the equation for this line?

[mScientist]

Hint: The point C lies on the line passing through A and B. How would one go about writing down the equation for this line?

 

I can solve this easily if it was 2D (only x and y).

2D Linear equation would be :

 

y = k*x + m

 

and

 

k = (y₂ - y₁) / (x₂ - x₁)

 

m = y - k*x

 

But I don't know how to deal with if it was 3D with (x,y,z).

Do you know how?

thanks

[Shadow]

You should first learn how to express a line in three dimensions; have a look here. For this specific problem, I would recommend the parametric expression, but to get a better grip on the subject it might not be a bad idea to try and solve this problem using all three expressions.