(Solved): Electromagnetic Theory \[ \begin{array}{l} \mathbf{A}=A_{x} \hat{\mathbf{a}}_ ...

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Electromagnetic Theory \[ \begin{array}{l} \mathbf{A}=A_{x} \hat{\mathbf{a}}_{x}+A_{y} \hat{\mathbf{a}}_{y}+A_{z} \hat{\mathbf{a}}_{z} \\ \mathbf{B}=B_{x} \hat{\mathbf{a}}_{\mathrm{x}}+\mathrm{B}_{\mathrm{y}} \hat{\mathbf{a}}_{y}+\mathrm{B}_{z} \hat{\mathbf{a}}_{z} \\ \mathbf{C}=\mathrm{C}_{\mathrm{x}} \hat{\mathbf{a}}_{\mathrm{x}}+\mathrm{C}_{\mathrm{y}} \hat{\mathbf{a}}_{\mathrm{y}}+\mathrm{C}_{\mathrm{z}} \hat{\mathbf{a}}_{\mathrm{z}} \end{array} \] including three separate vectors; 1) \( \vec{A}(\vec{B} \cdot \vec{C}) \neq(\vec{A} \cdot \vec{B}) \vec{C} \) 2) \( (\vec{A} \cdot \vec{B}) \vec{C}=\vec{C}(\vec{A} \cdot \vec{B}) \) Show clearly and proving that