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)

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- December 12th 2010, 11:06 AMdivinelogosOrthogonality
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) - December 12th 2010, 11:11 AMsnowtea
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. - December 12th 2010, 01:19 PMdivinelogos
Is magnitude the same as length?

- December 12th 2010, 02:03 PMsnowtea
Yes, magnitude of a vector is normally expressed by length.

- December 13th 2010, 03:30 AMHallsofIvy
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.