The set of quantities are components of an dimensional vector iff, under rotation,
(1)

for , 2, ..., . The direction cosines between and are
(2)

They satisfy the orthogonality condition
(3)

where is the Kronecker delta.
The set of quantities are components of an dimensional vector iff, under rotation,
(1)

for , 2, ..., . The direction cosines between and are
(2)

They satisfy the orthogonality condition
(3)

where is the Kronecker delta.
Weisstein, Eric W. "Vector Transformation Law." From MathWorldA Wolfram Web Resource. https://mathworld.wolfram.com/VectorTransformationLaw.html