How Is the Shortest Distance Between Two Vectors Determined?

[nokia8650]

Say you have two vectors: a and b.

Is the shortest distance between these two vectors when a line perpendicular to a meets vector b, or when a line perpendicular to vector b meets vector a?

Thanks

 

[tiny-tim]

Say you have two vectors: a and b.

Is the shortest distance between these two vectors when a line perpendicular to a meets vector b, or when a line perpendicular to vector b meets vector a?

Thanks

Hi nokia8650!

The length of one line is a.cosθ, and of the other is b.cosθ.

But those are the distances between one line and the other endpoint.

There is no such thing as the distance between two vectors … only between their endpoints.