Vector as Sum of Orthogonal Base Vectors
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Theorem
Let $\mathbf v$ be a vector quantity in ordinary $3$-space.
Let $\mathbf i, \mathbf j, \mathbf k$ be orthonormal base vectors.
Then:
- $\mathbf v = \paren {\mathbf v \cdot \mathbf i} \mathbf i + \paren {\mathbf v \cdot \mathbf j} \mathbf j + \paren {\mathbf v \cdot \mathbf k} \mathbf k$
Proof
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Sources
- 1961: I.N. Sneddon: Fourier Series ... (previous) ... (next): Chapter One: $\S 8$. Orthonormal Sets of Functions