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)?

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- Jan 18th 2011, 01:13 AMabrahamtimparametric 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 AMAckbeet
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 AMabrahamtim
- Jan 18th 2011, 02:02 AMAckbeetQuote:

How do you get v and b?