Übung: Vektoren addieren
randRangeNonZero( -9, 9 )
randRangeNonZero( -9, 9 )
randRangeNonZero( -9, 9 )
randRangeNonZero( -9, 9 )
Was ist \vec a + \vec b?
\begin{align*}
\vec a &= AX \hat\imath + AY \hat\jmath \\
\vec b &= BX \hat\imath + BY \hat\jmath
\end{align*}
graphInit({
range: 10,
scale: 20,
tickStep: 1,
labelStep: 1,
unityLabels: false,
labelFormat: function( s ) { return "\\small{" + s + "}"; },
axisArrows: "<->"
});
line( [0, 0], [AX, AY], { stroke: MatheguruHelper.BLUE, arrows: "->" } );
line( [0, 0], [BX, BY], { stroke: MatheguruHelper.PINK, arrows: "->" } );
var AF = 1 + 0.8 / sqrt( AX * AX + AY * AY );
label( [AF * AX, AF * AY], "\\vec a", { color: "#6495ed" } );
var BF = 1 + 0.8 / sqrt( BX * BX + BY * BY );
label( [BF * BX, BF * BY], "\\vec b", { color: "#28ae7b" } );
AX + BX
AY + BY
\hat\imath + {}\hat\jmathAddiere die \hat\imath und \hat\jmath Komponenten einzeln.
\hat a + \hat b = (AX + BX) \hat\imath + (AY + BY) \hat\jmath
line( [BX, BY], [BX + AX, BY + AY], { stroke: MatheguruHelper.PURPLE, arrows: "->" } );
\hphantom{\hat a + \hat b} = AX + BX\hat\imath + AY + BY\hat\jmath
line( [0, 0], [BX + AX, BY + AY], { stroke: MatheguruHelper.ORANGE, arrows: "->" } );