NMT / ZNO

Formulas and reference

A compact mathematics reference in two levels: the NMT exam sheet and the full ZNO formula set.

ZNO — full reference · Geometry · 6 formulas
Full ZNO Expanded school formula set. The “NMT” badge marks formulas also present on the compact sheet.
Vectors

Vectors

Coordinates of vector AB

NMT
\[\overrightarrow{AB}=(x_2-x_1;\,y_2-y_1;\,z_2-z_1)\]
10–11 grade

Vector length

\[|\vec a|=\sqrt{a_1^2+a_2^2+a_3^2}\]
10–11 grade

Dot product in coordinates

NMT
\[\vec a\cdot\vec b=a_1b_1+a_2b_2+a_3b_3\]
9–11 grade

Dot product using the angle

NMT
\[\vec a\cdot\vec b=|\vec a||\vec b|\cos\varphi\]
9–11 grade

Perpendicular vectors

\[\vec a\perp\vec b\Longleftrightarrow\vec a\cdot\vec b=0\]
9–11 grade

Collinear vectors in the plane

\[a_1b_2-a_2b_1=0\]
9–11 grade