Calculate constant vector, Macroeconomics

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A particle at position I with velocity i has acceleration w given by

i = w x (wxi)

where?is a constant vector. Show by using the vector triple product and calculating i - I that

v² + W²I²τ = constant

where v = |w|, I = |w|, τ = |w- n(I - n ) | and n is a unit vector in the direction of w

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