C2.8

solve problems involving dot product and cross product (e.g., determining projections, the area of a parallelogram, the volume of a parallelepiped), including problems arising from real-world applications (e.g., determining work, torque, ground speed, velocity, force) Sample problem: Investigate the dot products $\vec{a}\cdot (\vec{a}\times \vec{b})$ and $\vec{b}\cdot (\vec{a}\times \vec{b})$ for any two vectors $\vec{a}$ and $\vec{b}$ in three-space. What property of the cross product $\vec{a}\times \vec{b}$ does this verify?