if vector a cross vector b is equal to vector b cross vector c then prove vector a plus vector b plus vector c is equal to zero
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Geometric meaning
Given two unit vectors, their cross product has a magnitude of 1 if the two are perpendicular and a magnitude of zero if the two are parallel. The dot product of two unit vectors behaves just oppositely: it is zero when the unit vectors are perpendicular and 1 if the unit vectors are parallel.
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