Vektor $\overrightarrow{AB}=\vec{B}-\vec{A}\backslash overrightarrow\{AB\}=\backslash vec\; B-\backslash vec\; A$

Betrag des Vektors $\vec{A}=\sqrt{a_1^2+a_2^2+a_3^2}\backslash vec\; A=\backslash sqrt\{a\_1^2+a\_2^2+a\_3^2\}$

Mittelpunkt $MM$ einer Strecke $[AB][AB]$: $\vec{M}=\mathrm{0,5}\cdot (\vec{A}+\vec{B})\backslash vec\; M=0\{,\}5\backslash cdot(\backslash vec\; A+\backslash vec\; B)$

Skalarprodukt $\vec{a}\circ \vec{b}=a_1{b}_1+a_2{b}_2+a_3{b}_3\backslash vec\; a\backslash circ\; \backslash vec\; b=a\_1b\_1+a\_2b\_2+a\_3b\_3$

Vektor $\vec{a}\perp \vec{b}\backslash vec\; a\; \backslash perp\; \backslash vec\; b$: $\vec{a}\circ \vec{b}=0\backslash vec\; a\backslash circ\; \backslash vec\; b=0$

$\vec{a}\backslash vec\; a$ und $\vec{b}\backslash vec\; b$ linear abhängig: $\vec{a}=k\cdot \vec{b}\backslash vec\; a=k\backslash cdot\; \backslash vec\; b$

Winkel zwischen $\vec{a}\backslash vec\; a$ und $\vec{b}\backslash vec\; b$: $\cos (\alpha )={\displaystyle \frac{\vec{a}\circ \vec{b}}{\mathrm{\mid }\vec{a}\mathrm{\mid }\cdot \mathrm{\mid }\vec{b}\mathrm{\mid }}}\backslash cos(\backslash alpha)=\backslash dfrac\{\backslash vec\; a\backslash circ\; \backslash vec\; b\}\{|\backslash vec\; a|\backslash cdot|\backslash vec\; b|\}$

Kreuzprodukt $\vec{a}\backslash vec\; a$ und $\vec{b}\backslash vec\; b$: $\vec{a}\times \vec{b}\backslash vec\; a\backslash times\; \backslash vec\; b$