Thread: finding the parametric equation of a line

question: Find the parametric equation of the line through the points (0,.5,1) and (2,1,-3)

work:r=r_0+tv the vector parallel to the line is <2-0,1-.5,-3-1> I thought I would take (0,.5,1) to be the r_0 but the text book didn't. How do I know which initial point to use?

Am I doing this right? I mean is it necessary to find the vector equation and then from that take the parametric equation or is there a faster way?

Originally Posted by superdude

question: Find the parametric equation of the line through the points (0,.5,1) and (2,1,-3)

work:r=r_0+tv the vector parallel to the line is <2-0,1-.5,-3-1> I thought I would take (0,.5,1) to be the r_0 but the text book didn't. How do I know which initial point to use?

Am I doing this right? I mean is it necessary to find the vector equation and then from that take the parametric equation or is there a faster way?

the equation of a line passing through two points is

so your saying the problem can't be solved using the formula I was using?

Hi

Actually , we are talking the same method but my is the simplier expression :

We can take either or
to be the

After we calculate the vector parallel to the required line , we put the parameter [tex] t ATH] next to the vector and add up with or , the sum is what we are looking for

Don't believe ?

if we take to be the initial point

the required equation is

now if we take to be the initial point ,
the equation becomes


Well , obviously , they are totally different but if we change the parameter t by (t+1) , the equation (2) becomes

I don't think you found the direction vector right, it's point b-a not a-b