In an oblique basis with

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Tensors and differential geometry · Tensors and differential geometry

Invariance, Ch General bases, the metric and tensors in spacetime

Problem

|\mathbf{e}_1| = 2.0\,\mathrm{m}

|\mathbf{e}_2| = 3.0\,\mathrm{m}

and an angle of

50^\circ

between

\mathbf{e}_1

and

\mathbf{e}_2

, two vectors have contravariant components

A^i = (2, 1)

and

B^i = (1, 3)

. ((a)) Find the lengths

|\mathbf{A}|

and

|\mathbf{B}|

. ((b)) Find the angle between

\mathbf{A}

and

\mathbf{B}

using

\cos\theta = g_{ij}A^iB^j/(|\mathbf{A}||\mathbf{B}|)

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