Question

What is the angle between two identical unit vectors?

Answer 1

The angle between two identical unit vectors is Zero.

• When au and bu are the vector of units pointing in either direction, where the equivalent is the angle between the two vectors. This formula automatically includes the fact that the dot product of perpendicular vectors is always zero.
• au · bu  =  cos θ. where θ is an angle between two vectors. This formula automatically includes that the dot product of perpendicular vectors is zero as cos 90° is zero.
• Since two identical vectors create a degenerate parallelogram without an field, the cross-product of any vector with itself is zero. Extending this corollary to the unit vectors implies that any unit vector's cross-product with itself is zero