Object Disoriented 🤸‍♂️

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# The angle between lines and planes

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