Thread: Orthogonality

Do vectors have to touch to be considered orthogonal? For example, are both of these considered orthogonal?


1. T (the horizontal part of the "t" is a vector and the vertical part is a vector)

2. |
_______


(both lines are vectors)

Remember vectors have only a direction and magnitude.
They are not located at any position in space, so it doesn't make sense to say when two vectors are "touching"

Two vectors are orthogonal when their directions are orthogonal.

You can "move" a vector around. As long as it has the same direction and magnitude, it is the same vector.

Is magnitude the same as length?

Yes, magnitude of a vector is normally expressed by length.

We use the word "magnitude" because not all applications of vectors are "geometric". For example the "magnitude" of a velocity vector is speed, not length.