Demonstrate the property of BAC-CAB: \((\mathbf{a} \times \mathbf{b}) \times \mathbf{c}=\mathbf{b}(\mathbf{a} \cdot \mathbf{c})-\mathbf{c}(\mathbf{a} \cdot \mathbf{b})\), verifying it by direct development after arranging the vector \(\mathbf{c}\) along the \(x\) axis and the vector \(\mathbf{b}\) in the plane \((x, y)\).