Angle Between 2 Vectors Restrictions

Question

When finding the angle between 2 vectors, why does the angle have to be greater than or equal to 0 and less than or equal to pi(180 degrees)?

Answer 1

A vector has only two properties

1. Magnitude
2. Direction

Although directions can be expressed as angles in relation to a standard direction, a direction is not the same thing as an angle.

An angle may have any size and may have positive or negative sign. This is essential when measuring, for example, a rotation.

But the angle between two vectors is defined as the minimum non-negative angle separating their directions. That angle cannot exceed a value of $\pi$ radians or $180^\circ$.