By the angle between lines and planes, we mean $\angle(\text{line}, \text{line})$, $\angle(\text{plane}, \text{plane})$, and $\angle(\text{line}, \text{plane})$.
| !../assets/img/060323-135707.svg | 060323-135707 |
The angle $v$ between two lines is the same as the angle $u$ between the directional vectors $\vec{r_{l}}$ and $\vec{r_{m}}$ of the lines $l$ and $m$.
Alternatively $v = 180^{\circ} - u$, such that $v \in [0^{\circ}, 90^{\circ}]$, because we always want to find the smallest angle.
The angle $v$ between two planes is the same as the angle $u$ between the perpendicular vectors of the planes.
Alternatively $v = 180^{\circ} - u$, such that $v \in [0^{\circ}, 90^{\circ}]$.
The angle $v$ between a line and a plane is defined by the angle $u$ between the directional vectors of the line and the perpendicular vector of the plane.
Alternatively $v = 90^{\circ} - u$ or $v = u - 90^{\circ}$, such that $v \in [0^{\circ}, 90^{\circ}]$.
| We use the ./Skalarproduktet | scalar product to calculate these angles. |
| !../Skalarprodukt | Skalarprodukt |