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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