C2.6

perform the operation of cross product on two vectors represented in Cartesian form in three-space [i.e., using $\vec{a}\times \vec{b}=(a_2{b}_3-a_3{b}_2,a_3{b}_1-a_1{b}_3,a_1{b}_2-a_2{b}_1)$], determine the magnitude of the cross product (i.e., using $|\vec{a}\times \vec{b}|=|\vec{a}||\vec{b}|\sin \theta$), and describe applications of the cross product (e.g., determining a vector orthogonal to two given vectors; determining the turning effect [or torque] when a force is applied to a wrench at different angles) Sample problem: Explain how you maximize the torque when you use a wrench and how the inclusion of a ratchet in the design of a wrench helps you to maximize the torque.