Math problem (vector calculus)?
Can someone please explain to me how I can solve this problem?
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Du sollst testen, ob die Punkte A oder B auf der jeweiligen Geraden liegen.
Beispiel:
A (1│0│-2)
Wenn der Punkt A auf der Geraden liegt, gibt es einen Wert für r, der die Koordinaten von A ergibt. Stelle also 3 Gleichungen auf, bestimme aus der ersten Gleichung r und prüfe, ob die zweite und dritte Gleichung zu den gegebenen Komponenten von A führt.
(1) 1 + 2r = 1
(2) 0 + 4r = 0
(3) -2 + 2r = 2
————————
(1) 2r = 0
(1) r = 0
(2) 0 + 4 * 0 = 0 (passt)
(3) -2 + 2 * 0 = -2 (passt nicht)
Punkt A liegt also nicht auf der Geraden.
…
Setze die Koordinaten der gegebenen 2 Punkte statt “x” ein und finde jeweils Werte für r,s,k,l . Wenn sich ein Wert finden lässt, liegt der Punkt auf der Geraden. Wenn nicht, dann nicht.
You can form the position vector of the points by making the coordinates the components of respective vectors.
You can then substitute the vector for x.
Then you calculate the position vector of the line.
You can then use the result to form a system of equations.
This yields a scalar result if the points lie on the line. Otherwise, you won't get a true statement.