Difference between revisions of "The Cross Product"

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[[File:Cross product parallelogram.svg|Cross_product_parallelogram]]
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[[File:Cross product parallelogram.svg|thumb|Cross_product_parallelogram]]
 
The cross product is an operation between two 3-dimensional vectors that returns a third vector orthogonal (i.e., perpendicular) to the first two. For vectors <math> \mathbf{u} = \langle u_1, u_2, u_3 \rangle </math> and <math> \mathbf{v} = \langle v_1, v_2, v_3 \rangle </math>, the cross product of <math> \mathbf{u} </math> and <math> \mathbf{v} </math> (notated as <math> u \times v </math>) is <math> \mathbf{w} =  \langle u_2v_3 - u_3v_2, -(u_1v_3 - u_3v_1), u_1v_2 - u_2v_1 \rangle</math>.
 
The cross product is an operation between two 3-dimensional vectors that returns a third vector orthogonal (i.e., perpendicular) to the first two. For vectors <math> \mathbf{u} = \langle u_1, u_2, u_3 \rangle </math> and <math> \mathbf{v} = \langle v_1, v_2, v_3 \rangle </math>, the cross product of <math> \mathbf{u} </math> and <math> \mathbf{v} </math> (notated as <math> u \times v </math>) is <math> \mathbf{w} =  \langle u_2v_3 - u_3v_2, -(u_1v_3 - u_3v_1), u_1v_2 - u_2v_1 \rangle</math>.
  
<math> \begin{vmatrix} a & b \\ c & d \end{vmatrix} </mode>
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<math> \begin{vmatrix} a & b \\ c & d \end{vmatrix} </math>
  
 
==Resources==
 
==Resources==
 
* [https://openstax.org/books/calculus-volume-3/pages/2-4-the-cross-product The Cross Product], OpenStax
 
* [https://openstax.org/books/calculus-volume-3/pages/2-4-the-cross-product The Cross Product], OpenStax
 
* [https://omega0.xyz/omega8008/calc3/cross-product-dir/cornell-lecture.html Cross Product], Cornell University
 
* [https://omega0.xyz/omega8008/calc3/cross-product-dir/cornell-lecture.html Cross Product], Cornell University

Revision as of 17:21, 20 September 2021

Cross_product_parallelogram

The cross product is an operation between two 3-dimensional vectors that returns a third vector orthogonal (i.e., perpendicular) to the first two. For vectors and , the cross product of and (notated as ) is .

Resources