Cross product is proportional to sine of angle between vectors¶
The cross product of two vectors is a binary operation which produces a vector whose length is proportional to the lengths of the given vectors and the sine of the angle between them.
Links:
- cross_product_length¶
Length of the cross product between \(\vec u\) and \(\vec v\).
- Symbol:
norm(cross(u, v))- Latex:
\(\left \Vert \left[ \vec u, \vec v \right] \right \Vert\)
- Dimension:
any_dimension
- first_vector_length¶
Length of \(\vec u\).
- Symbol:
u- Latex:
\(u\)
- Dimension:
any_dimension
- second_vector_length¶
Length of \(\vec v\).
- Symbol:
v- Latex:
\(v\)
- Dimension:
dimensionless
- Symbol:
phi- Latex:
\(\varphi\)
- Dimension:
angle
- law¶
norm(cross(u, v)) = u * v * sin(phi)- Latex:
- \[\left \Vert \left[ \vec u, \vec v \right] \right \Vert = u v \sin{\left(\varphi \right)}\]