Exercise
https://texercises.com/exercise/durchstosspunkt-von-gerade-durch-ebene/
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Exercise:
Bestimme den Durchstosspunkt der Geraden g leftarrayc a aa aaa arrayright + lambda leftarrayc b bb bbb arrayright auf der Ebene E: x x + y y + z z r.

Solution:
split g leftarrayc a aa aaa arrayright + lambda leftarrayc b bb bbb arrayright x a + b lambda y aa + bb lambda z aaa + bbb lambda E: r x x + y y + z z x a + b lambda + y aa + bb lambda + z aaa + bbb lambda lambda thenumexpr x * a + b + y * aa + bb + z * aaa + bbb relax g leftarrayc a aa aaa arrayright + thenumexpr x * a + b + y * aa + bb + z * aaa + bbb relax leftarrayc b bb bbb arrayright leftarrayc thenumexpr a + x * a + b + y * aa + bb + z * aaa + bbb * b relax thenumexpr aa + x * a + b + y * aa + bb + z * aaa + bbb * bb relax thenumexpr aaa + x * a + b + y * aa + bb + z * aaa + bbb * bbb relax arrayright split
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\(\LaTeX\)-Code
Exercise:
Bestimme den Durchstosspunkt der Geraden g leftarrayc a aa aaa arrayright + lambda leftarrayc b bb bbb arrayright auf der Ebene E: x x + y y + z z r.

Solution:
split g leftarrayc a aa aaa arrayright + lambda leftarrayc b bb bbb arrayright x a + b lambda y aa + bb lambda z aaa + bbb lambda E: r x x + y y + z z x a + b lambda + y aa + bb lambda + z aaa + bbb lambda lambda thenumexpr x * a + b + y * aa + bb + z * aaa + bbb relax g leftarrayc a aa aaa arrayright + thenumexpr x * a + b + y * aa + bb + z * aaa + bbb relax leftarrayc b bb bbb arrayright leftarrayc thenumexpr a + x * a + b + y * aa + bb + z * aaa + bbb * b relax thenumexpr aa + x * a + b + y * aa + bb + z * aaa + bbb * bb relax thenumexpr aaa + x * a + b + y * aa + bb + z * aaa + bbb * bbb relax arrayright split
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Tags
durchstosspunkt, ebene, gerade, mathematik, punkt, vektorgeometrie
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Difficulty
(1, default)
Points
0 (default)
Language
GER (Deutsch)
Type
Calculative / Quantity
Creator uz
Decoration
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Link