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Reference.org
Vector algebra relations
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<p>The following are important identities in <a href="/facts/Vector_space/M1pxMLx2">vector algebra</a>. Identities that only involve the magnitude of a vector ‖ A ‖ {\displaystyle \|\mathbf {A} \|} and the <a href="/facts/Dot_product/tNz8MLjT">dot product</a> (scalar product) of two vectors A·B, apply to vectors in any dimension, while identities that use the <a href="/facts/Cross_product/uRBJzkcW">cross product</a> (vector product) A×B only apply in three dimensions, since the cross product is only defined there. Most of these relations can be dated to founder of vector calculus <a href="/facts/Josiah_Willard_Gibbs/xyWwxQtA">Josiah Willard Gibbs</a>, if not earlier. </p>