What are orthonormal vectors? Show that two non-null, orthogonal vectors are linearly independent.

Orthonormal vectors are a set of vectors that are both orthogonal and normalized. This means that each vector in the set is perpendicular (orthogonal) to every other vector in the set, and each vector has a unit length (normalized). In mathematical terms, for two vectors \( \vec{a} \) and \( \vec{b} \), they are orthonormal if:

1. \( \vec{a} \cdot \vec{b} = 0 \) (orthogonality condition),
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