# Homework Help: Points on a 3D vector

1. Aug 3, 2009

### fenpark15

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!

2. Aug 3, 2009

### slider142

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.

3. Aug 3, 2009

### tiny-tim

Hi fenpark15!

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).