Difference between revisions of "The Cross Product"
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The cross product of <math> \mathbf{u} </math> and <math> \mathbf{v} </math> can also be written in determinant form like so: | The cross product of <math> \mathbf{u} </math> and <math> \mathbf{v} </math> can also be written in determinant form like so: | ||
| − | <math>\mathbf{w} = det\begin{vmatrix} | + | <math>\mathbf{w} = \textrm{det}\begin{vmatrix} |
i & j & k\\ | i & j & k\\ | ||
u_1 & u_2 & u_3\\ | u_1 & u_2 & u_3\\ | ||
Revision as of 17:27, 20 September 2021
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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{v} = \langle v_1, v_2, v_3 \rangle } , the cross product of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{u} } and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{v} } (notated as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle u \times v } ) is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{w} = \langle u_2v_3 - u_3v_2, -(u_1v_3 - u_3v_1), u_1v_2 - u_2v_1 \rangle} . The cross product of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{u} } and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{v} } can also be written in determinant form like so:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{w} = \textrm{det}\begin{vmatrix} i & j & k\\ u_1 & u_2 & u_3\\ v_1 & v_2 & v_3\\ \end{vmatrix} }
Resources
- The Cross Product, OpenStax
- Cross Product, Cornell University
