ElI5 What is the difference between the vector form of a line and the parametric form?

Question

ElI5 What is the difference between the vector form of a line and the parametric form?

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Answer 1

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.