Is it possible for the product of two non-zero vectors to be zero?
2 Answers
Yes, if you are referring to dot product or to cross product.
Explanation:
The dot product of any two orthogonal vectors is
The cross product of any two collinear vectors is
Note that for any two non-zero vectors, the dot product and cross product cannot both be zero.
There is a vector context in which the product of any two non-zero vectors is non-zero. It is known as Hamilton's Quaternions. Quaternions form a
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It is possible to get a zero-magnitude resultant vector for both dot-product and cross-product vector multiplication.
Explanation:
Vector multiplication is usually defined as being one of either the dot-product (sometimes called the inner or scalar product) or a cross-product (sometimes called the outer or vector product). In each case it is possible to get a zero-magnitude result.
Dot Product:
The dot-product of two vectors
where
which means that the result is zero if the vectors are perpendicular to each other
Cross Product:
the cross-product of two vectors
where the result is a vector pointing in the direction
which means that the result is zero if the vectors are parallel to each other