Question

How should we describe a line in space using Algebra?

Hint:

1. We can think of a plane as a collection of vectors in space which satisfies an equation of the form ax + by + cz = d. False, because we can move vectors around, which will mess up the plane.
2. We can think of a plane as a collection of vectors in space whose starting point must be at the origin which satisfies an equation of the form ax + by + cz = d. True, because fixing where the vectors starts (i.e., at the origin) means we can't move the vectors around.

Answer 1