Izračunavanje presjeka
uredi
Presjek dvije prave u dvodimenzionalnom prostoru
uredi
Presjek dvije prave
L
1
{\displaystyle L_{1}\,}
L
2
{\displaystyle L_{2}\,}
dvodimenzionalnom prostoru gdje je prava
L
1
{\displaystyle L_{1}\,}
(
x
1
,
y
1
)
{\displaystyle (x_{1},y_{1})\,}
(
x
2
,
y
2
)
{\displaystyle (x_{2},y_{2})\,}
L
2
{\displaystyle L_{2}\,}
(
x
3
,
y
3
)
{\displaystyle (x_{3},y_{3})\,}
(
x
4
,
y
4
)
{\displaystyle (x_{4},y_{4})\,}
determinante .[2]
T
{\displaystyle T}
T
x
=
|
|
x
1
y
1
x
2
y
2
|
|
x
1
1
x
2
1
|
|
x
3
y
3
x
4
y
4
|
|
x
3
1
x
4
1
|
|
|
|
x
1
1
x
2
1
|
|
y
1
1
y
2
1
|
|
x
3
1
x
4
1
|
|
y
3
1
y
4
1
|
|
T
y
=
|
|
x
1
y
1
x
2
y
2
|
|
y
1
1
y
2
1
|
|
x
3
y
3
x
4
y
4
|
|
y
3
1
y
4
1
|
|
|
|
x
1
1
x
2
1
|
|
y
1
1
y
2
1
|
|
x
3
1
x
4
1
|
|
y
3
1
y
4
1
|
|
{\displaystyle T_{x}={\frac {\begin{vmatrix}{\begin{vmatrix}x_{1}&y_{1}\\x_{2}&y_{2}\end{vmatrix}}&{\begin{vmatrix}x_{1}&1\\x_{2}&1\end{vmatrix}}\\\\{\begin{vmatrix}x_{3}&y_{3}\\x_{4}&y_{4}\end{vmatrix}}&{\begin{vmatrix}x_{3}&1\\x_{4}&1\end{vmatrix}}\end{vmatrix}}{\begin{vmatrix}{\begin{vmatrix}x_{1}&1\\x_{2}&1\end{vmatrix}}&{\begin{vmatrix}y_{1}&1\\y_{2}&1\end{vmatrix}}\\\\{\begin{vmatrix}x_{3}&1\\x_{4}&1\end{vmatrix}}&{\begin{vmatrix}y_{3}&1\\y_{4}&1\end{vmatrix}}\end{vmatrix}}}\,\!\qquad T_{y}={\frac {\begin{vmatrix}{\begin{vmatrix}x_{1}&y_{1}\\x_{2}&y_{2}\end{vmatrix}}&{\begin{vmatrix}y_{1}&1\\y_{2}&1\end{vmatrix}}\\\\{\begin{vmatrix}x_{3}&y_{3}\\x_{4}&y_{4}\end{vmatrix}}&{\begin{vmatrix}y_{3}&1\\y_{4}&1\end{vmatrix}}\end{vmatrix}}{\begin{vmatrix}{\begin{vmatrix}x_{1}&1\\x_{2}&1\end{vmatrix}}&{\begin{vmatrix}y_{1}&1\\y_{2}&1\end{vmatrix}}\\\\{\begin{vmatrix}x_{3}&1\\x_{4}&1\end{vmatrix}}&{\begin{vmatrix}y_{3}&1\\y_{4}&1\end{vmatrix}}\end{vmatrix}}}\,\!}
gdje
T
x
{\displaystyle T_{x}}
T
y
{\displaystyle T_{y}}
koordinate u datoj ravni . Prethodni determinanti se također ujedinjeno mogu napisati kao torka :
(
T
x
,
T
y
)
=
(
(
x
1
y
2
−
y
1
x
2
)
(
x
3
−
x
4
)
−
(
x
1
−
x
2
)
(
x
3
y
4
−
y
3
x
4
)
(
x
1
−
x
2
)
(
y
3
−
y
4
)
−
(
y
1
−
y
2
)
(
x
3
−
x
4
)
,
(
x
1
y
2
−
y
1
x
2
)
(
y
3
−
y
4
)
−
(
y
1
−
y
2
)
(
x
3
y
4
−
y
3
x
4
)
(
x
1
−
x
2
)
(
y
3
−
y
4
)
−
(
y
1
−
y
2
)
(
x
3
−
x
4
)
)
{\displaystyle {\begin{aligned}(T_{x},T_{y})={\bigg (}&{\frac {(x_{1}y_{2}-y_{1}x_{2})(x_{3}-x_{4})-(x_{1}-x_{2})(x_{3}y_{4}-y_{3}x_{4})}{(x_{1}-x_{2})(y_{3}-y_{4})-(y_{1}-y_{2})(x_{3}-x_{4})}},\\&{\frac {(x_{1}y_{2}-y_{1}x_{2})(y_{3}-y_{4})-(y_{1}-y_{2})(x_{3}y_{4}-y_{3}x_{4})}{(x_{1}-x_{2})(y_{3}-y_{4})-(y_{1}-y_{2})(x_{3}-x_{4})}}{\bigg )}\end{aligned}}}
Također pogledajte
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Nedovršeni članak Presjek dvije prave matematici treba dopuniti. Dopunite ga pravilima Wikipedije.
Nedovršeni članak Presjek dvije prave koji govori o matematici treba dopuniti. Dopunite ga prema pravilima Wikipedije.