Many of the physical quantities that will be described in this course are vectors. For instance, force, velocity, acceleration, and electric field are vectors.
You must be able to:
add two vectors, $\vec{A}+\vec{B}=(A_x+B_x)\hat{x}+ (A_y+B_y)\hat{y}+ (A_z+B_z)\hat{z}$;
determine the length of a vector, $|\vec{A}|=\sqrt{A_x^2+A_y^2+A_z^2}$;
determine the unit vector pointing in the same direction as a vector, $\hat{A}=\frac{\vec{A}}{\left|\vec{A}\right|}$;
decompose a vector into its $x$-, $y$-, and $z$-components;
calculate the inner product of two vectors, $\vec{A}\cdot\vec{B}=\left|\vec{A}\right|\left|\vec{B}\right|\cos(\theta)=A_xB_x+A_yB_y+A_zB_z$;
calculate the cross product of two vectors, $\vec{A}\times\vec{B}=(A_yB_z-A_zB_y)\hat{x}+ (A_zB_x-A_xB_z)\hat{y}+ (A_xB_y-A_yB_x)\hat{z}$.
