For example, dotting a vector \(\mathbf{A}\) with any of the cartesian unit vectors gives the projection of \(\mathbf{A}\) in that direction: In general, the projection of vector \(\mathbf{A}\) in the...For example, dotting a vector \(\mathbf{A}\) with any of the cartesian unit vectors gives the projection of \(\mathbf{A}\) in that direction: In general, the projection of vector \(\mathbf{A}\) in the direction of unit vector \(\hat{\mathbf{u}}\) is \(\mathbf{A} \cdot \hat{\mathbf{u}}\). From Eq. (7.2.6), it follows that \(\mathbf{A} \cdot \mathbf{A}=A_{x}^{2}+A_{y}^{2}+A_{z}^{2}=A^{2}\); so the magnitude of a vector \(\mathbf{A}\) is given in terms of the dot product by
