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Basis vectors and the metric tensor

This video goes through the process of deriving the basis vectors in an arbitrary coordinate system and then looks at how these basis vectors are related to the metric for the space. Correction: At 12:15 the formula for the angle between two vectors should NOT have a square root in the numerator. The correct form is: Cos(𝜃) = g_ij u^i v^j / [Sqrt(g_ij u^i u^j) Sqrt(g_ij v^i v^j)]