# Dictionary:Cross product

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1. A type of vector multiplication. If i, j, and k are mutually orthogonal unit vectors so that two vectors A and B may be expressed in terms of components in these directions:

${\displaystyle {\textbf {A}}=a_{1}{\textbf {i}}+a_{2}{\textbf {j}}+a_{3}{\textbf {k}}\;}$

and

${\displaystyle {\textbf {B}}=b_{1}{\textbf {i}}+b_{2}{\textbf {j}}+b_{3}{\textbf {k}}}$

then the cross product A×B is orthogonal to both A and B:

${\displaystyle {\textbf {A}}\times {\textbf {B}}=(a_{2}b_{3}-a_{3}b_{2}){\textbf {i}}+(a_{3}b_{1}-a_{1}b_{3}){\textbf {j}}+(a_{1}b_{2}-a_{2}b_{1}){\textbf {k}}}$

Also called outer product.

2. The terms in an algebraic multiplication that involves elements of different kinds; e.g., ${\displaystyle 2ab}$ is the cross product term in ${\displaystyle (a+b)^{2}=a^{2}+2ab+b^{2}}$.