9. The scalar product





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 = u_{1}i + u_{2}j + u_{3}k, v = v_{1}i + v_{2}j + v_{3}k and w = w_{1}i + w_{2}j + w_{3}k. Then
Alternatively one could prove the algebraic rules using the Cartesian representation of the scalar product.


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