9. The scalar product
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Suppose u, v and w are vectors (in the plane or in space) with magnitudes |u|, |v| and |w|. Then
The rules are obtained by using the Cartesian representation of the scalar product. We let u = u1i + u2j + u3k, v = v1i + v2j + v3k and w = w1i + w2j + w3k. Then
Alternatively one could prove the algebraic rules using the Cartesian representation of the scalar product.
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