Alright, let's say you want to get from one point to another, in a 3D box. all points have an x, y and z coordinate. Point A has coordinates (25,30,5) while Point B has coordinates (50,26,18). The only given variable other than the coordinates is the speed you are traveling. What is an equation I can use to first find the distance between the two points, and then the time it would take to travel between the two at a fixed speed?

Question

Alright, let's say you want to get from one point to another, in a 3D box.  all points have an x, y and z coordinate.  Point A has coordinates (25,30,5) while Point B has coordinates (50,26,18).  The only given variable other than the coordinates is the speed you are traveling.  What is an equation I can use to first find the distance between the two points, and then the time it would take to travel between the two at a fixed speed?

Reiny · Answer

the formula for distance in 3D follows the same pattern as the distance in 2D

Dist = √((delta x)^2 + (delta y)^2 + (delta z)^2)

so Dist = √(25^2 + (-4)^2 + 13^2)
= √810

Time = Distance/Rate would still apply for the time.