 Solution

ID: past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2014-resit/11/a/solution

Write

ω = (ω_{x}, ω_{y}, ω_{z})

v = (ω_{y} z - ω_{z} y, ω_{z} x - ω_{x} z, ω_{x} y - ω_{y} x)

. Since the components of

ω

are constant, direct partial differentiation gives

\nabla \times v = (ω_{x} - (- ω_{x}), ω_{y} - (- ω_{y}), ω_{z} - (- ω_{z})) = 2 ω .

Thus

ω = \frac{1}{2} \nabla \times v .

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