Can someone help me with calculating cartesian coordinates for a moving object?

[Ralgar]

Hi. I was just wondering if anyone could help me with a formula to solve the following problem.

I have two locations (L1 and L2), which I know the cartesian coordinates of, situated in a three dimensional space. I also have a distance (D) which I also know the value of. D is not the distance between L1 and L2. If an object moves from it's starting location at L1 in a straight line towards L2, how do I calculate the cartesian coordinates of the object after it has traveled a distance of D units.

I'd certainly appreciate any assistance in this.

Cheers.

 

[HallsofIvy]

Let L₁= (x₁,y₁,z₁) and
L₂= (x₂,y₂,z₂).

Let d= distance from L₂ to L₁= [sqrt]((x₂-x₁)²+(y₂-y₁)²+(z₂-z₁)²).

The any point on the line through L₂ and L₁ has coordinates
x= x₁+ (x₂-x₁)(t/d)
y= y₁+ (y₂-y₁(t/d)
z= z₁+ (z₂-z₁)(t/d)

(notice that when t= 0, this is x= x₁ and when t= d, this is x= x₂, etc.)

In particular, taking t= D will give the coordinates of the point at distance D from L₁ in the direction of L₂.

 

[Ralgar]

Thank you.