Unit Vectors of Cartesian 3-Space form Basis

Theorem

Consider the Cartesian $3$-space $C$.

Let $\mathbf i$, $\mathbf j$ and $\mathbf k$ denote the unit vectors in the positive directions of the $x$-axis, $y$-axis and $z$-axis respectively.

Then $\set {\mathbf i, \mathbf j, \mathbf k}$ forms a basis for $C$.

Proof

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Sources

• 1970: George Arfken: Mathematical Methods for Physicists (2nd ed.) ... (previous) ... (next): Chapter $1$ Vector Analysis $1.1$ Definitions, Elementary Approach