MathLiveCross product
Gives the vector perpendicular to two vectors in three-dimensional space, with magnitude equal to the area of the parallelogram they span. It is used in geometry, mechanics and electromagnetism, for example to compute torque or normal directions.
\boldsymbol{a} \times \boldsymbol{b} = \begin{pmatrix} a_y b_z - a_z b_y \\ a_z b_x - a_x b_z \\ a_x b_y - a_y b_x \end{pmatrix}What the symbols mean
| first input vector, with components a_x, a_y, a_z | |
| second input vector, with components b_x, b_y, b_z | |
| Cartesian components of the first vector | |
| Cartesian components of the second vector |
About this formula
- FieldMathematics
- TopicVector algebra
- LevelHigh school
- Also calledvector product, cross product of two vectors, cross product formula, vector cross product components, a cross b, Levi-Civita cross product
- SourceWikidata Q178192
Write it in Obsidian
MathLive is a free visual math editor for Obsidian. Run Find a formula, type “cross product”, and it goes into your note as editable LaTeX. You can also scan formulas from screenshots, PDFs and handwriting.