This video shows the scalar and parametric equations for how to write equations of lines in three dimensions and explains where the formulas come from.
Now I understand why I struggled with vectors. I didn't get my basics right. We can solve problema by just memoriziny the formula. But for 3D geometry once we cross a certain level of difficulty of problems, it is impossible to solve without the concepts. Thanks ❤
A vector has initial point and it can extend in only one direction,but a line can extend in both directions then how a vector(r vector)can represent a line
The vector for the line has a parameter "t" which then makes it represent infinite vectors (choose as many values for t as you want). Without the parameter (variable), you are right, it's just a vector pointing to one place and not a line. The idea is that for every "t" value, the vector's terminal point is at a new location on a line. So, you run through all possible t-values and then it draws the line! Kind of like how y=mx+b is a line in 2D space. So, if you have something like y=2x+3...for every x-value you input, you get a new y-value on the line. This just uses "x" instead of "t."
I won't lie this is the best explanation I've found on the internet
I had lost hope in understanding planes-
Thank you!
So glad I could help!
thanks so much our teacher didnt told us these basics and we were directly into question solving
I’m glad I could help explain some of these concepts!
Thank you for great explanation.
Now I understand why I struggled with vectors. I didn't get my basics right. We can solve problema by just memoriziny the formula. But for 3D geometry once we cross a certain level of difficulty of problems, it is impossible to solve without the concepts. Thanks ❤
This channel is great
Thank you!
it,s a good video on internet and also easy understandable
This video explains it in a way so that it becomes easy as cake! 🍰🤠
A vector has initial point and it can extend in only one direction,but a line can extend in both directions then how a vector(r vector)can represent a line
The vector for the line has a parameter "t" which then makes it represent infinite vectors (choose as many values for t as you want). Without the parameter (variable), you are right, it's just a vector pointing to one place and not a line.
The idea is that for every "t" value, the vector's terminal point is at a new location on a line. So, you run through all possible t-values and then it draws the line!
Kind of like how y=mx+b is a line in 2D space. So, if you have something like y=2x+3...for every x-value you input, you get a new y-value on the line. This just uses "x" instead of "t."
@@DrClaireMath thanks a lot🤗🤗