Got a real eureka moment watching this. The equation of a line in 3d is composed of 3 equations of lines in 2d. Please correct if I'm wrong, but for 2d we only got the relation between the x- and y-axis (one relation). Thus in 3d we have 3 relations x-y, x-z and y-z and hence 3 "2d- line equations", one for each relation. Thank you very much!
I love eureka moments! Actually, if we drop the z, we would have parametric equations for a line in 2D. There would be two of them x = x_0 + at and y = y_0 + bt. What we know as the slope m would be b/a. I hope this helps.
Take the distance formula and plug the x, y, and z in from the parametric equation of the line (the formulas in t). Set that distance formula equal to desired distance and solve for t. That will be the “time” that you’re at that desired point. Lastly, take that time back into the parametric equations to find the point. Let me know if you have further questions or if you need a further explanation.
@@NakiaRimmer Firstly, that's awesome that you took the time to reply back on a 3 year old video. Secondly if i'm being honest, this comes from a video game, but is a great thing to learn. The game's GPS points are measured in meters and so i have two points P0(0,0,0) and P1(-1537682.47, 946785.7, 437077.2). My overall goal is to be able to plot a point, lets say 1000KM away from P1, but along the same line that P0 and P1 are on. My math and physics skills so far are pretty much crash course upon discovery(attempt to learn from any material i come across, very little foundation). The distance from P0 to P1, according to my fancy excel skills with the distance formula, is 1857.93. When you say the parametric equations, im assuming its something like this: www.math.usm.edu/lambers/mat169/fall09/lecture25.pdf?
This was so easy to understand! Thank you for making this simple and clear.
Very well spoken and great pace. Thank you!
Got a real eureka moment watching this. The equation of a line in 3d is composed of 3 equations of lines in 2d. Please correct if I'm wrong, but for 2d we only got the relation between the x- and y-axis (one relation). Thus in 3d we have 3 relations x-y, x-z and y-z and hence 3 "2d- line equations", one for each relation.
Thank you very much!
I love eureka moments! Actually, if we drop the z, we would have parametric equations for a line in 2D. There would be two of them x = x_0 + at and y = y_0 + bt. What we know as the slope m would be b/a. I hope this helps.
Very clear and easily understood,,, it really helped y
You are a great teacher and reminds me of my high school math teacher! Excellent and very clear explanation! 👍
youre saving me in my linear algebra uni class rn
Great explanation! Thanks. Just subscribed.
Thank you, this really helped.
Wow, that was super helpful! Thank you .
Great work sir ❤
thanks a lot, it was so helpful.
How best can you determine these from a 2D image like a photograph?
Great explanation
What if i wanted to find a point on that line in space where the origin and P0 are on the same line and you have a specified distance?
Take the distance formula and plug the x, y, and z in from the parametric equation of the line (the formulas in t). Set that distance formula equal to desired distance and solve for t. That will be the “time” that you’re at that desired point. Lastly, take that time back into the parametric equations to find the point. Let me know if you have further questions or if you need a further explanation.
@@NakiaRimmer Firstly, that's awesome that you took the time to reply back on a 3 year old video. Secondly if i'm being honest, this comes from a video game, but is a great thing to learn. The game's GPS points are measured in meters and so i have two points P0(0,0,0) and P1(-1537682.47, 946785.7, 437077.2). My overall goal is to be able to plot a point, lets say 1000KM away from P1, but along the same line that P0 and P1 are on. My math and physics skills so far are pretty much crash course upon discovery(attempt to learn from any material i come across, very little foundation). The distance from P0 to P1, according to my fancy excel skills with the distance formula, is 1857.93. When you say the parametric equations, im assuming its something like this: www.math.usm.edu/lambers/mat169/fall09/lecture25.pdf?
Can you use the other point
Yes, the set of parametric equations for a line is not unique. You can use any point on the line and any multiple of the vector
what if given two vectors?
Two vectors determine a plane when paired with a point in the plane. Let me know if I can help further
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