ElI5 What is the difference between the vector form of a line and the parametric form?
In: 1
The vector form is still in the form y=f(x) = a*x + b, except a and b are multidimensional vectors. The parameterization is of the form y=f1(s), x=f2(s)
Edit: This was not simple enough, so let’s dig deeper.
Let’s think about what y=f(x) means.
Imagine a rollercoaster in 2D. It goes up and down, accelerates, and decelerates. The vector form is like the first-person POV, and the parameterization is the third-person POV
Vector form is like telling someone the road’s direction and giving them a point on the road. For example, you’d say, “Go in the direction of this arrow, and start from this spot.”
Parametric form, on the other hand, is like telling someone how far they’ve traveled on the road from the starting point. You’d say, “After driving for 5 miles, you’ll be at this point.”
So, the vector form tells you the direction and a point on the line, while the parametric form tells you how far you’ve gone from the starting point to reach a certain spot on the line. They’re two different ways to describe the same line.
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