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diff --git a/mat/domace_naloge/26/dokument.tex b/mat/domace_naloge/26/dokument.tex index 2871afb..691a83e 100644 --- a/mat/domace_naloge/26/dokument.tex +++ b/mat/domace_naloge/26/dokument.tex @@ -148,24 +148,28 @@ Ta dokument vsebuje navodila in rešitve domačih nalog snovi \textit{\snovdn}pr \tkzDrawPolygon[fill=red!30, opacity=.3](A,B,C) \tkzDrawSegments[vect](A,B A,C) \end{tikzpicture} + $$\Vec{c}\cdot\Vec{b}=|\Vec{c}|\cdot|\Vec{b}|=9\cdot\cos{\ang{60}}=4,5$$ \task v enakostraničnem trikotniku s stranico, dolgo \cm{3}, \begin{tikzpicture}[vect/.style={->,shorten >=0pt,>=latex'}] \tkzDefPoint(0,0){A} \tkzDefPoint(3,0){B} \tkzDefPoint(60:3){C} \tkzDrawPolygon[fill=red!30, opacity=.3](A,B,C) \tkzDrawSegments[vect](C,A B,C) \end{tikzpicture} + $$\Vec{a}\cdot\Vec{b}=|\Vec{a}|\cdot|\Vec{b}|\cdot\cos{\left(\ang{180}-\ang{60}\right)}=-4,5$$ \task v pravokotniku s stranicama, dolgima \cm{6} in \cm{2}, \begin{tikzpicture}[vect/.style={->,shorten >=0pt,>=latex'}] \tkzDefPoint(0,0){A} \tkzDefPoint(6,0){B} \tkzDefPoint(6,2){C} \tkzDefPoint(0,2){D} \tkzDrawPolygon[fill=red!30, opacity=.3](A,B,C,D) \tkzDrawSegments[vect](A,B B,C) \end{tikzpicture} + $$\Vec{a}\cdot\Vec{b}=|\Vec{a}|\cdot|\Vec{b}|\cdot\cos{\ang{90}}=0$$ \task v pravokotniku s stranicama, dolgina \cm{6} in \cm{2}, \begin{tikzpicture}[vect/.style={->,shorten >=0pt,>=latex'}] \tkzDefPoint(0,0){A} \tkzDefPoint(6,0){B} \tkzDefPoint(6,2){C} \tkzDefPoint(0,2){D} \tkzDrawPolygon[fill=red!30, opacity=.3](A,B,C,D) \tkzDrawSegments[vect](A,B A,C) \end{tikzpicture} + $$\vektor{b}\cdot\vektor{e}=|\vektor{b}|\cdot|\vektor{e}|\cdot\cos{\left(\sqrt{\cm{6}^2+\cm{2}^2}\right)}\Dot=11,926966$$ \task v pravilnem 6-kotniku s stranico, dolgo \cm{2}, \begin{tikzpicture}[vect/.style={->,shorten >=0pt,>=latex'}] @@ -174,6 +178,7 @@ Ta dokument vsebuje navodila in rešitve domačih nalog snovi \textit{\snovdn}pr \tkzDrawPolygon[fill=red!30, opacity=.3](P1,P2,P3,P4,P5,P6) \tkzDrawSegments[vect](P2,P1 P2,P3) \end{tikzpicture} + $$\vektor{P_1P_2}\cdot\vektor{P_2P_3}=|\vektor{P_1P_2}|\cdot|\vektor{P_2P_3}|\cdot\cos{\ang{120}}=-2$$ \task v pravilnem 6-kotniku s stranico, dolgo \cm{2}. \begin{tikzpicture}[vect/.style={->,shorten >=0pt,>=latex'}] @@ -182,11 +187,20 @@ Ta dokument vsebuje navodila in rešitve domačih nalog snovi \textit{\snovdn}pr \tkzDrawPolygon[fill=red!30, opacity=.3](P1,P2,P3,P4,P5,P6) \tkzDrawSegments[vect](P1,P6 P3,P2) \end{tikzpicture} + $$\Vec{P_6P_1}\cdot\Vec{P_3P_2}=|\Vec{P_6P_1}|\cdot|\Vec{P_3P_2}|\cdot\cos{\ang{120}}=-2$$ \end{tasks} \item Kocka $ABCDA'B'C'D'$ ima \cm{10} dolg rob. Izračunaj $\vektor{AB}\cdot\vektor{AC}$, $\vektor{AB}\cdot\vektor{AC'}$, $\vektor{AD'}\cdot\vektor{AC'}$, $\vektor{BD'}\cdot\vektor{DB'}$. + $$\vektor{AB}\cdot\vektor{AC}=\cm{10}\cdot\cm{10}\cdot\cos{\ang{45}}=50$$ + $$\vektor{AB}\cdot\vektor{AC'}=\cm{10}\cdot\sqrt{\cm{10}^2+\cm{10}^2}\cdot\cos{\ang{45}}=70,710678$$ + $$\vektor{AD'}\cdot\vektor{AC'}=\cm{10}\cdot\sqrt{\cm{10}^2+\cm{10}^2}\cdot\cos{\ang{45}}=100$$ + $$\vektor{BD'}\cdot\vektor{DB'}=\sqrt{\cm{10}^2+\cm{10}^2}\cdot\sqrt{\cm{10}^2+\cm{10}^2}\cos\ang{45}=100$$ \item Tetraeder $ABCD$ ima \cm{10} dolg rob. Izračunaj $\vektor{AB}\cdot\vektor{AC}$, $\vektor{AB}\cdot\vektor{AD}$, $\vektor{AD}\cdot\vektor{AD}$. + \def\kot{70,528779} + $$\vektor{AB}\cdot\vektor{AC}=\cm{10}\cdot\cm{10}\cdot\cos\arccos\frac{1}{3}=33,\overline{3}$$ + $$\vektor{AB}\cdot\vektor{AD}=\cm{10}\cdot\cm{10}\cdot\cos\arccos\frac{1}{3}=33,\overline{3}$$ + $$\vektor{AD}\cdot\vektor{AD}=100$$ \end{enumerate} \section{Zaključek} Ta dokument je informativne narave in se lahko še spreminja. Najnovejša različica, torej PDFji in |