Euclidean Geometry #2

Geometry Level pending

In the three dimensional space R 3 R^3 ,let's considerate S to be the surface of the triangle with vertex A(1,2,-1), B(3,4,0) and C(4,2,2). Find 2S


The answer is 9.

Guillermo Templado by Guillermo Templado , 46, Spain

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1 solution

A(1,2,-1), B(3,4,0), C(4,2,2) ⇒ \Rightarrow A B → \overrightarrow{AB} = (2,2,1), A C → \overrightarrow{AC} = (3,0,3) ⇒ \Rightarrow 2S = | A B → \overrightarrow{AB} x A C → \overrightarrow{AC} | (module of the cross "vectorial" product of A B → \overrightarrow{AB} and A C → \overrightarrow{AC} ) ; A B → \overrightarrow{AB} x A C → \overrightarrow{AC} = (6,-3,-6) ⇒ \Rightarrow 2S = | A B → \overrightarrow{AB} x A C → \overrightarrow{AC} |= | (6,-3,-6) | = 9 . Coming soon another solution, maybe

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