VC3.7

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Let a=a_1 i+a_2 j+a_3 k\,

Also \nabla =i\frac{\partial}{\partial x}+j\frac{\partial}{\partial y}+k\frac{\partial}{\partial z}\,

Hence a\cdot\nabla=a_1\frac{\partial}{\partial x}+a_2\frac{\partial}{\partial y}+a_3\frac{\partial}{\partial z}\,

So, (a\cdot\nabla)\phi=a_1\frac{\partial \phi}{\partial x}+a_2\frac{\partial \phi}{\partial y}+a_3\frac{\partial \phi}{\partial z}\, [Equation 1]

Again a\cdot\nabla\phi=(a_1 i+a_2 j+a_3 k)\cdot[\frac{\partial \phi}{\partial x}i+j\frac{\partial \phi}{\partial y}+k\frac{\partial \phi}{\partial z}\,

=a_1\frac{\partial \phi}{\partial x}+a_2\frac{\partial \phi}{\partial y}+a_3\frac{\partial \phi}{\partial z}\, [Equation 2]

From (1) and (2),(a\cdot \nabla)\phi=a\cdot \nabla \phi\,

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