In this video I show that if the dot or cross products are zero then neither vector has to be zero, but if BOTH the dot and cross products are zero then at least one of the vectors has to be zero. If the dot product is zero, then it just means the two vectors are perpendicular to each other. If the cross product is zero, then it just means the two vectors are parallel. But if both the dot and cross products are zero, then the only way for the two vectors to both be perpendicular and parallel is if one of the vectors is a zero vector.
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