VC3.13

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a\cdot \nabla =[(x+3y)i+(y-3z)j+(x-2z)k]\cdot [i{\frac  {\partial }{\partial x}}+j{\frac  {\partial }{\partial y}}+k{\frac  {\partial }{\partial z}}]\,

=(x+3y){\frac  {\partial }{\partial x}}+(y-3z){\frac  {\partial }{\partial y}}+(x-2z){\frac  {\partial }{\partial z}}\,

Now,(a\cdot \nabla )a=[(x+3y){\frac  {\partial }{\partial x}}+(y-3z){\frac  {\partial }{\partial y}}+(x-2z){\frac  {\partial }{\partial z}}][(x+3y)i+(y-3z)j+(x-2z)k]\,

=(x+3y){\frac  {\partial }{\partial x}}[(x+3y)i+(y-3z)j+(x-2z)k]+(y-3z){\frac  {\partial }{\partial y}}[(x+3y)i+(y-3z)j+(x-2z)k]+{\frac  {\partial }{\partial z}}[(x+3y)i+(y-3z)j+(x-2z)k]\,

=(x+3y)(i+k)+(y-3z)(3i+j)+(x-2z)(-3j-2k)\,

=[(x+3y)+3(y-3z)]i+[(y-3z)-(3(x-2z)]j+[(x+3y)-2(x-2z)]k\,

=(x+6y-9z)i+(-3x+y+3z)j+(-x+3y+4z)k\,

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