Hello! Great question. In 2 dimensions a vertical line has equation x = k for some constant k. There is no mention of y in the equation at all. This means that y is free to be anything you want but x is stuck on k. So you would parametrize it by have x = k and y = t. You would allow t to go from your smallest y to your largest y if it is a line segment. If it is the entire line, then t would go from -infinity to infinity. Let me know if you were asking about a vertical line in 3 dimensions.
@@NakiaRimmer Yes, I was asking in two dimensions, thanks. And if the parametrized line, for example, starts from (2;2) and ends in (0;2), how would parametrize it? Is it y=2, x=t?
@@toniocartonio572 Yes, but the issue you run into is that t starts at 2 and end at 0. t is going backwards, usually you want t to go forwards. What you can do is let x =-t and then t would go from -2 to 0. The thing with parametrizations is that there is no unique way to do it, so you should parametrize whichever way is easiest for you.
@12:20 : r(t) should have 3-4t in the first component
Thank you SO much! Things that have confused me for a long time finally click when I hear you explain them!
Thank you‼️
You are an outstanding teacher! Thank you for this video!
wow! well explained and helpful, thanks, Mr.Rimmer!!
Am so greatiful, thanks so so so so much....I have clearly understood line integrals....
Fantastic explanation!
thank you mr Rimmer very helpful, and i am glad to have found your videos :)
amazing video sir
you saved my semester I was about to drop my class because it did not understand parametrization
sobrang maestra ito
Great video😊
Hi, how do you parametrize a vertical line? Great vid btw
Hello! Great question. In 2 dimensions a vertical line has equation x = k for some constant k. There is no mention of y in the equation at all. This means that y is free to be anything you want but x is stuck on k. So you would parametrize it by have x = k and y = t. You would allow t to go from your smallest y to your largest y if it is a line segment. If it is the entire line, then t would go from -infinity to infinity. Let me know if you were asking about a vertical line in 3 dimensions.
@@NakiaRimmer Yes, I was asking in two dimensions, thanks. And if the parametrized line, for example, starts from (2;2) and ends in (0;2), how would parametrize it? Is it y=2, x=t?
@@toniocartonio572 Yes, but the issue you run into is that t starts at 2 and end at 0. t is going backwards, usually you want t to go forwards. What you can do is let x =-t and then t would go from -2 to 0. The thing with parametrizations is that there is no unique way to do it, so you should parametrize whichever way is easiest for you.
For the ending isn't x=3-4t why did you put 3+4t in your parameterized vector r(t)= < 3+4t, 2+6t, 1+6t > ?
Yes, thank you for catching that mistake. I’ll pin a comment with the correction.
Great video, very well explained and very helpful as well, thanks!