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?
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