Définition vectorielle du volume d'un tétraède

"Volume de OABC " = 1/6 (vec(a) "," vec(b) "," vec(c))

"avec"

vec(a) ((a_x),(a_y),(a_z)) " , " vec(b) ((b_x),(b_y),(b_z)) " , " vec(b) ((c_x),(c_y),(c_z))

(vec(a) "," vec(b) "," vec(c))

= (vec(a) ^^ vec(b)) . vec(c)

= det(vec(a) "," vec(b) "," vec(c))

= c_x|(a_y,b_y),(a_z,b_z)| - c_y|(a_x,b_x),(a_z,b_z)| + c_z|(a_x,b_x),(a_y,b_y)|        

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