Past exam of the mathematical methods II course of the University of Oxford / 2016 resit / 3 / i

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- Solution i

Solution

In Cartesian components,

a \cdot r = a_{x} x + a_{y} y + a_{z} z

, with constant

a_{i}

. Taking the gradient component by component gives

\nabla (a \cdot r) = a .

The constancy of

a

matters: if it depended on position, derivatives of its components would also contribute.

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