What do you suppose is the direction of the vector represented by:

(4, 0)^{T}

The vector is parallel to the X axis of the coordinate frame we are using. Often this is horizontal, pointing right. (Or, you might have said that the vector is oriented at 0 degrees.)

A 2D vector that is aligned with a coordinate axis,
as with (4, 0)^{T},
has an orientation
that is easy to see.
It is 0 degrees, 90 degrees,
180 degrees, or 270 degrees.

The orientation of a vector is usually expressed as an angle with the positive x axis of a coordinate frame. There are two ways of doing this:

- The angle is 0° to 360° measured as a counter-clockwise rotation from the positive x axis.
- The angle is 0° to +180° measured as a counter-clockwise rotation from the positive x axis, or is 0° to -180° measured as a clockwise rotation from the positive x axis,

What is the direction of **a** ?