when will the cross product of two vectors be zero
Cross product If two vectors have the same direction (or have the exact opposite direction from one another, i.e. are not linearly independent) or if either one has zero length, then their cross product is zero. More generally, the magnitude of the product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two perpendicular vectors is the product of their lengths. The cross product is anticommutative (i.e.,   a × b = − b × a  {\displaystyle \mathbf {a} \times \mathbf {b} =-\mathbf {b} \times \mathbf {a} } ) and is distributive over addition (i.e.,   a × ( b + c ) = a × b + a × c  {\displaystyle \mathbf {a} \times (\mathbf {b} +\mathbf {c} )=\mathbf {a} \times \mathbf {b} +\mathbf {a} \times \mathbf {c} } ). The space    R  3   {\displaystyle \mathbb {R} ^{3}}  together with the cross product is an algebra over the real numbers, which is neither commutative nor associative, but is a Lie algebra with the cross product being the Lie bracket.
Hermitian matrix The diagonal elements must be real, as they must be their own complex conjugate.
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g-force Human tolerances depend on the magnitude of the g-force, the length of time it is applied, the direction it acts, the location of application, and the posture of the body.[7][8]:350