I have the following triangle coordinates: A=(0,1/2,3/2) B=(1,1,0) C=(1,0,1) How can I calculate the perimeter of the triangle ABC ?

joguejaseg 2022-09-16 Answered
I have the following triangle coordinates:
A = ( 0 , 1 / 2 , 3 / 2 )
B = ( 1 , 1 , 0 )
C = ( 1 , 0 , 1 )
How can I calculate the perimeter of the triangle ABC ?
Should I add the vertices of the triangle like this?
A B : ( 0 1 ) 2 + ( 1 / 2 1 ) 2 + ( 3 / 2 0 ) 2
B C : ( 1 1 ) 2 + ( 1 0 ) 2 + ( 0 1 ) 2
C A : ( 1 0 ) 2 + ( 0 1 / 2 ) 2 + ( 1 3 / 2 ) 2
And how can I calculate the value of the internal angle of C?
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Answers (1)

ahem37
Answered 2022-09-17 Author has 15 answers
If you want to use vectors, find vectors C B and C A:
The components of C B are (0,1,−1), C A are (−1,0.5,0.5). Then you can find length (magnitude) of the vectors, i.e. : | | C B | | = 0 2 + 1 2 + ( 1 ) 2 .
To find cosine of the angle C, use the law of cosines:
cos C = C A C B | | C A | | | | C B | |
where C A C B = 0 ( 1 ) + 1 0.5 + ( 1 ) 0.5 = 0 is the "dot" product.

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