Thread: parametric equation of a line in R^4

1. parametric equation of a line in R^4

How do you find the parametric equation of a line in $R^4$ that passes through the points (1,2,3,4) and (5,6,7,8)?

2. Well, the general form of a line in any dimensions looks like this:

$\mathbf{y}=t\,\mathbf{v}+\mathbf{b},$

where $\mathbf{v}$ is a vector parallel to the line, and $\mathbf{b}$ is a vector from the origin to a point on the line. How could you get $\mathbf{v}$ and $\mathbf{b}?$

3. Originally Posted by Ackbeet
Well, the general form of a line in any dimensions looks like this:

$\mathbf{y}=t\,\mathbf{v}+\mathbf{b},$

where $\mathbf{v}$ is a vector parallel to the line, and $\mathbf{b}$ is a vector from the origin to a point on the line. How could you get $\mathbf{v}$ and $\mathbf{b}?$
How do you get v and b ?

4. How do you get v and b?
That's what I just asked you! Think to yourself: I've got two points on the line. There should be a way, from that information alone, to get a vector parallel to the line. What do you suppose that method is?