C2.4

perform the operation of dot product on two vectors represented as directed line segments (i.e., using $\vec{a}\cdot \vec{b}=|\vec{a}||\vec{b}|\cos \theta$) and in Cartesian form (i.e., using $\vec{a}\cdot \vec{b}=a_1{b}_1+a_2{b}_2$ or $\vec{a}\cdot \vec{b}=a_1{b}_1+a_2{b}_2+a_3{b}_3$) in two-space and three-space, and describe applications of the dot product (e.g., determining the angle between two vectors; determining the projection of one vector onto another) Sample problem: Describe how the dot product can be used to compare the work done in pulling a wagon over a given distance in a specific direction using a given force for different positions of the handle.