Mathematics · Ch 6 — Applications of Vector Algebra

Scalar Product and Vector Product

6.3

Definition 6.1. For $\vec a=a_1\hat i+a_2\hat j+a_3\hat k$ and $\vec b=b_1\hat i+b_2\hat j+b_3\hat k$ :

the scalar product (dot product) is $\vec a\cdot\vec b=a_1b_1+a_2b_2+a_3b_3$ — a scalar;
the vector product (cross product) is

\vec a\times\vec b=\begin{vmatrix}\hat i&\hat j&\hat k\\ a_1&a_2&a_3\\ b_1&b_2&b_3\end{vmatrix} = (a_2b_3-a_3b_2)\hat i-(a_1b_3-a_3b_1)\hat j+(a_1b_2-a_2b_1)\hat k,

a vector. …