Dot Product: An operation that takes two equal-length sequences of numbers and returns a single number. It is calculated as $\mathbf{A} \cdot \mathbf{B} = A_x B_x + A_y B_y + A_z B_z$ for three-dimensional vectors.
Cross Product: A binary operation on two vectors in three-dimensional space resulting in another vector perpendicular to the plane containing the original vectors. Given by $\mathbf{A} \times \mathbf{B}$.
Unit Vector: A vector with a magnitude of one. Often used to indicate direction only without regard to magnitude.