Consider vectors A and B (not parallel to each other). In a rotated coordinate system (compared to an original coordinate system), all of the following remain unchanged except
A) A · B.
B) A $\times$ B.
C) |A| and |B|.
D) the components of A and the components of B.

Question

Quizplus · Accepted Answer

The dot product (A · B), the cross product magnitude (|A $\times$ B|), and the magnitudes of vectors (|A| and |B|) are invariant under rotation of the coordinate system. However, the components of vectors A and B themselves will change in a rotated coordinate system, as these depend on the basis vectors of the coordinate system.

Consider Vectors a and B (Not Parallel to Each Other) ×\times×

Consider Vectors a and B (Not Parallel to Each Other) $\times$