# Vector equations

## Homework Statement

What is the significance of each vector forumula? Which one is used for what and why? What is the purpose of the symmetric function?

## Homework Equations

1) r = r0 + tv
2) r(t) = (1 - t)r0 + tr1
3) Symmetric equation

## The Attempt at a Solution

My textbook introduced me to the first formula write equations for vectors, which I understand. Later it introduced segments and modified the first equation to the second one, without any clear explanation. I don't understand why seperate formulas are needed for vectors and segments. Finally, my textbook concluded that chapter by eliminating the parameter t and getting the "symmetric equation". What is the purpose of that equation? Thank you so much. This is so confusing for me.

Related Calculus and Beyond Homework Help News on Phys.org
jedishrfu
Mentor
The first one describes a particle at position r0 at time t0=0 moving with velocity v. The r then is the position at any time t of the particle.

The second one is saying given a particle at r0 and then at r1 you can determine its position at any time t.

Notice when you rearrange the terms a bit you get r0 + (r1 - r0) t so the (r1 - r0) factor is the velocity v from the first equation.

I'm not sure about the symmetric equation...