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.
Victoria Cross The Victoria Cross (VC) is the highest and most prestigious award of the British honours system. It is awarded for gallantry "in the presence of the enemy" to members of the British Armed Forces. It may be awarded posthumously. It was previously awarded to Commonwealth countries, most of which have established their own honours systems and no longer recommend British honours. It may be awarded to a person of any military rank in any service and to civilians under military command although no civilian has received the award since 1879. Since the first awards were presented by Queen Victoria in 1857, two thirds of all awards have been personally presented by the British monarch. These investitures are usually held at Buckingham Palace.