97. Later in our sudy of physics we will encounter quantities represented by $(\overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}}) \cdot \overrightarrow{\boldsymbol{C}}$, (a) Prove that for any three vectors $\vec{A}, \vec{B}$, and $\overrightarrow{\boldsymbol{C}}, \overrightarrow{\boldsymbol{A}} \cdot(\overrightarrow{\boldsymbol{B}} \times \overrightarrow{\boldsymbol{C}})=(\overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}}) \cdot \overrightarrow{\boldsymbol{C}}$ (b) Calculate $(\vec{A} \times \vec{B}) \cdot \vec{C}$ for the three vectors $\vec{A}$ with magnitude $A=5.00$ and angle $\theta_{A}=26.0^{\circ}$ measured in the sense from the $+x$-axis toward the $+y$-axis, $\vec{B}$ with $B=4.00$ and $\theta_{B}=63.0^{\circ}$, and $\vec{C}$ with magnitude $6.00$ and in the $+z$-direction.

 97. Later in our sudy of physics we will encounter quantities represented by $(\overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}}) \cdot \overrightarrow{\boldsymbol{C}}$, (a) Prove that for any three vectors $\vec{A}, \vec{B}$, and $\overrightarrow{\boldsymbol{C}}, \overrightarrow{\boldsymbol{A}} \cdot(\overrightarrow{\boldsymbol{B}} \times \overrightarrow{\boldsymbol{C}})=(\overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}}) \cdot \overrightarrow{\boldsymbol{C}}$ (b) Calculate $(\vec{A} \times \vec{B}) \cdot \vec{C}$ for the three vectors $\vec{A}$ with magnitude $A=5.00$ and angle $\theta_{A}=26.0^{\circ}$ measured in the sense from the $+x$-axis toward the $+y$-axis, $\vec{B}$ with $B=4.00$ and $\theta_{B}=63.0^{\circ}$, and $\vec{C}$ with magnitude $6.00$ and in the $+z$-direction. Vectors $\overrightarrow{\boldsymbol{A}}$ and $\overrightarrow{\boldsymbol{B}}$ are in the $x y$-plane.