Winkel Zwischen Vektoren Beispiel Essay

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Wiederholung: Winkel zwischen Vektoren

Gesucht ist der Winkel \(\varphi\) („Phi“) zwischen den beiden Vektoren \(\vec{a}\) und \(\vec{b}\).

Formel zur Berechnung des Winkels zwischen zwei Vektoren

\[\varphi = \cos^{-1}\left(\frac{\vec{a}\circ\vec{b}}{\left|\vec{a}\right|\cdot\left|\vec{b}\right|}\right)\]

Anmerkungen

Das Symbol \(\varphi\) ist der griechische Kleinbuchstabe „Phi“.

\(\varphi\) ist in diesem Fall eine Bezeichnung für den Winkel zwischen \(\vec{a}\) und \(\vec{b}\).

\(\cos^{-1}\) ist die Umkehrfunktion der Kosinusfunktion, auch Arkuskosinus genannt.

\(\vec{a}\circ\vec{b}\) ist das Skalarprodukt der Vektoren.

\(|\vec{a}|\) und \(|\vec{b}|\) sind die Längen der Vektoren (> Betrag eines Vektors).

Beispiel

siehe Artikel Winkel zwischen zwei Vektoren

Online-Rechner: Winkel zwischen Vektoren

Im Folgenden erkläre ich dir kurz, wie der Rechner funktioniert. Mach dir keine Sorgen:
Du musst weder Mathe- noch Technik-Freak sein, um mit dem Teil zurechtzukommen ;)

Eingabe

Eingabefeld 1: Vektor 1
Eingabefeld 2: Vektor 2

Koordinaten werden durch Kommas voneinander getrennt.
Beispiel:(3,-4) (Bedeutung: \(\vec{v} = \begin{pmatrix} 3 \\ -4 \end{pmatrix}\))

Dezimalzahlen werden mit Punkt als Trennzeichen eingegeben.
Beispiel:(1,1.5,2) (Bedeutung: \(\vec{v} = \begin{pmatrix} 1 \\ 1{,}5 \\ 2 \end{pmatrix}\))

Bruchzahlen werden mit Schrägstrich eingeben.
Beispiel:(-1/3,3) (Bedeutung: \(\vec{v} = \begin{pmatrix} -\frac{1}{3} \\ 3 \end{pmatrix}\))

Ausgabe

Winkel zwischen den eingegebenen Vektoren in Grad

Beispiel

Berechne den Winkel zwischen \(\vec{a} = \begin{pmatrix} 1 \\ 0 \end{pmatrix}\) und \(\vec{b} = \begin{pmatrix} 1 \\ 1 \end{pmatrix}\).

Um das Beispiel zu berechnen, kannst du einfach auf „Winkel berechnen“ klicken!
(Ich habe die Werte aus der Aufgabe für dich bereits in den Rechner eingegeben.)

Weitere Online-Rechner zu diesem Thema

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