Classical Mechanics (Kibble & Berkshire) · Problem 1.10

Velocity, acceleration and scalar angular velocity — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · vector-algebra-triple-vector-product

Problem

By expressing the vectors

\boldsymbol{a}

\boldsymbol{b}

\boldsymbol{c}

in terms of a suitable standard basis, prove the identity

\boldsymbol{a}\times(\boldsymbol{b}\times\boldsymbol{c}) = (\boldsymbol{a} \cdot \boldsymbol{c})\boldsymbol{b} - (\boldsymbol{a} \cdot \boldsymbol{b})\boldsymbol{c}.