Understanding Vector Equations and Their Significance in Mathematics

[Calpalned]

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 separate 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.

 

[jedishrfu]

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...