# parametric equation of a line in R^4

• Jan 18th 2011, 01:13 AM
abrahamtim
parametric equation of a line in R^4
How do you find the parametric equation of a line in $\displaystyle R^4$ that passes through the points (1,2,3,4) and (5,6,7,8)?
• Jan 18th 2011, 01:35 AM
Ackbeet
Well, the general form of a line in any dimensions looks like this:

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

where $\displaystyle \mathbf{v}$ is a vector parallel to the line, and $\displaystyle \mathbf{b}$ is a vector from the origin to a point on the line. How could you get $\displaystyle \mathbf{v}$ and $\displaystyle \mathbf{b}?$
• Jan 18th 2011, 01:50 AM
abrahamtim
Quote:

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

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

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

How do you get v and b ?
• Jan 18th 2011, 02:02 AM
Ackbeet
Quote:

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?