= Solution
{c}
The <scalar product>, also called the <dot product>, and the <cross product>[vector product], also called the <cross product>, are
$$
\boxed{\mathbf a\cdot\mathbf b=a_1b_1+a_2b_2+a_3b_3,\qquad
\mathbf a\wedge\mathbf b=\begin{pmatrix}a_2b_3-a_3b_2\\a_3b_1-a_1b_3\\a_1b_2-a_2b_1\end{pmatrix}.}
$$
For nonzero <vectors>, let $\vartheta\in[0,\pi]$ be their <angle>. Their <Euclidean norms> satisfy
$$
\boxed{\mathbf a\cdot\mathbf b=|\mathbf a||\mathbf b|\cos\vartheta,\qquad
|\mathbf a\wedge\mathbf b|=|\mathbf a||\mathbf b|\sin\vartheta.}
$$
The <cross product> is <orthogonal> to both <vectors>, with its orientation determined by the <right-hand rule>. If either <vector> is zero, both products vanish, although the <angle> is undefined.
Back to article page
