[lern_too_spel]

This doesn't properly explain what it says it explains. To explain it correctly, you have to explain why the dot product of two vectors computed as the sum of the products of the coefficients of an orthonormal basis is a scalar equal to the product of the Euclidean magnitudes of the vectors and the cosine of the angle between them. The Wikipedia article on dot product explains this reasonably well, so just read that.