Finding Endpoints on a 3D Vector | Simple Method and Formula

  • Thread starter Thread starter fenpark15
  • Start date Start date
  • Tags Tags
    3d Points Vector
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
Sign up Log in
2 replies · 4K views
fenpark15
Messages
4
Reaction score
0
I'm trying to find the simplest way to locate points on a 3D vector.

I have 2 points (a,b,c) (d,e,f) which define a 3D vector. I know the midpoint between those points. [(a,b,c)+(d,e,f)]/2

I have a linear "object" with a known length L and I want to find the endpoints (u,v,w),(x,y,z) of that object centered at the midpoint and oriented along the vector.

Thanks!
 

Discussion

Physics news on Phys.org
It sounds like you want to find points on the line defined by the two points you mention first. In that case, note that every point x = (x, y, z) on that line satisfies the equation x = (d - a)s + a for some number s, where a = (a, b, c) and d = (d, e, f). After some thought you should see why. You should also then see that the constant vector a in the above equation can be any position vector on the line, including the "midpoint" you mentioned previously. Does this help with your question?
Of course, you can also do this geometrically, without referring to the algebraicization. Just draw the triangle created by the position vectors a and d and the rest should follow.
 
fenpark15 said:
I have a linear "object" with a known length L and I want to find the endpoints (u,v,w),(x,y,z) of that object centered at the midpoint and oriented along the vector.

Hi fenpark15! :smile:

Hint: If the centre is C, and the endpoints are A and D, then the new endpoints will be C ± a multiple of (D - A). :wink: