56. By making simple sketches of the appropriate vector products, show that $(a) \vec{A} \cdot \vec{B}$ can be interpreted as the product of the magnitude of ..

56. By making simple sketches of the appropriate vector products, show that $(a) \vec{A} \cdot \vec{B}$ can be interpreted as the product of the magnitude of $\overrightarrow{\boldsymbol{A}}$ times the component of $\overrightarrow{\boldsymbol{B}}$ along $\overrightarrow{\boldsymbol{A}}$, or the magnitude of $\vec{B}$ times the component of $\vec{A}$ along $\vec{B}$ (b) $|\overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}}|$ can be interpreted as the product of the magnitude of $\overrightarrow{\boldsymbol{A}}$ times the component of $\overrightarrow{\boldsymbol{B}}$ perpendicular to $\overrightarrow{\boldsymbol{A}}$, or the magnitude of $\overrightarrow{\boldsymbol{B}}$ times the component $\overrightarrow{\boldsymbol{A}}$ perpendicular to $\overrightarrow{\boldsymbol{B}}$