Area of a triangle in space using determinants from 3 points
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I know there is a way to find the area in plane using 3 points but when it comes to space(3D) does it work too? if so how should it look?
Thanks
area solid-geometry
edited Dec 24 '18 at 11:10
Bernard
124k743118
asked Dec 24 '18 at 10:52
Abdelrhman MahmoudAbdelrhman Mahmoud
11
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add a comment |
$begingroup$
I know there is a way to find the area in plane using 3 points but when it comes to space(3D) does it work too? if so how should it look?
Thanks
area solid-geometry
edited Dec 24 '18 at 11:10
Bernard
124k743118
asked Dec 24 '18 at 10:52
Abdelrhman MahmoudAbdelrhman Mahmoud
11
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You can see here: math.stackexchange.com/questions/427528/…
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– Emilio Novati
Dec 24 '18 at 10:56
1
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math.stackexchange.com/q/2152754/478643
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– Matko
Dec 24 '18 at 10:59
add a comment |
$begingroup$
I know there is a way to find the area in plane using 3 points but when it comes to space(3D) does it work too? if so how should it look?
Thanks
area solid-geometry
edited Dec 24 '18 at 11:10
Bernard
124k743118
asked Dec 24 '18 at 10:52
Abdelrhman MahmoudAbdelrhman Mahmoud
11
$endgroup$
I know there is a way to find the area in plane using 3 points but when it comes to space(3D) does it work too? if so how should it look?
Thanks
area solid-geometry
area solid-geometry
edited Dec 24 '18 at 11:10
Bernard
124k743118
asked Dec 24 '18 at 10:52
Abdelrhman MahmoudAbdelrhman Mahmoud
11
edited Dec 24 '18 at 11:10
Bernard
124k743118
asked Dec 24 '18 at 10:52
Abdelrhman MahmoudAbdelrhman Mahmoud
11
edited Dec 24 '18 at 11:10
Bernard
124k743118
edited Dec 24 '18 at 11:10
Bernard
124k743118
edited Dec 24 '18 at 11:10
Bernard
124k743118
124k743118
asked Dec 24 '18 at 10:52
Abdelrhman MahmoudAbdelrhman Mahmoud
11
asked Dec 24 '18 at 10:52
Abdelrhman MahmoudAbdelrhman Mahmoud
11
asked Dec 24 '18 at 10:52
Abdelrhman MahmoudAbdelrhman Mahmoud
11
11
$begingroup$
You can see here: math.stackexchange.com/questions/427528/…
$endgroup$
– Emilio Novati
Dec 24 '18 at 10:56
1
$begingroup$
math.stackexchange.com/q/2152754/478643
$endgroup$
– Matko
Dec 24 '18 at 10:59
add a comment |
$begingroup$
You can see here: math.stackexchange.com/questions/427528/…
$endgroup$
– Emilio Novati
Dec 24 '18 at 10:56
1
$begingroup$
math.stackexchange.com/q/2152754/478643
$endgroup$
– Matko
Dec 24 '18 at 10:59
$begingroup$
You can see here: math.stackexchange.com/questions/427528/…
$endgroup$
– Emilio Novati
Dec 24 '18 at 10:56
$begingroup$
You can see here: math.stackexchange.com/questions/427528/…
$endgroup$
– Emilio Novati
Dec 24 '18 at 10:56
1
1
$begingroup$
math.stackexchange.com/q/2152754/478643
$endgroup$
– Matko
Dec 24 '18 at 10:59
$begingroup$
math.stackexchange.com/q/2152754/478643
$endgroup$
– Matko
Dec 24 '18 at 10:59
add a comment |
1 Answer
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If you have three points $A,B,C$ you can form the vectors $AB$ and $AC$.
The norm of the cross product vector $ABtimes AC$ is twice the area of the triangle $ABC$
Since the cross product is found be a determinant, the area of a triangle could also be found by a determinant.
answered Dec 24 '18 at 11:17
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.1k42061
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1 Answer
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active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
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active
oldest
votes
$begingroup$
If you have three points $A,B,C$ you can form the vectors $AB$ and $AC$.
The norm of the cross product vector $ABtimes AC$ is twice the area of the triangle $ABC$
Since the cross product is found be a determinant, the area of a triangle could also be found by a determinant.
answered Dec 24 '18 at 11:17
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.1k42061
$endgroup$
add a comment |
$begingroup$
If you have three points $A,B,C$ you can form the vectors $AB$ and $AC$.
The norm of the cross product vector $ABtimes AC$ is twice the area of the triangle $ABC$
Since the cross product is found be a determinant, the area of a triangle could also be found by a determinant.
answered Dec 24 '18 at 11:17
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.1k42061
$endgroup$
add a comment |
$begingroup$
If you have three points $A,B,C$ you can form the vectors $AB$ and $AC$.
The norm of the cross product vector $ABtimes AC$ is twice the area of the triangle $ABC$
Since the cross product is found be a determinant, the area of a triangle could also be found by a determinant.
answered Dec 24 '18 at 11:17
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.1k42061
$endgroup$
If you have three points $A,B,C$ you can form the vectors $AB$ and $AC$.
The norm of the cross product vector $ABtimes AC$ is twice the area of the triangle $ABC$
Since the cross product is found be a determinant, the area of a triangle could also be found by a determinant.
answered Dec 24 '18 at 11:17
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.1k42061
answered Dec 24 '18 at 11:17
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.1k42061
answered Dec 24 '18 at 11:17
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.1k42061
answered Dec 24 '18 at 11:17
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.1k42061
42.1k42061
add a comment |
add a comment |
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You can see here: math.stackexchange.com/questions/427528/…
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– Emilio Novati
Dec 24 '18 at 10:56
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– Matko
Dec 24 '18 at 10:59