From the definition of cross product. v x u and u x v are two vectors that have opposite directions. So adding a '-' will let them be the same vector
winstonc
Swapping operands of the cross product can be seen as switching your fingers when using the right hand rule, so the resulting vectors should oppose each other.
emm
u x v and v x u are two vectors with the same magnitude but opposite directions, by the formal definition of the cross product, thus flipping the direction by making it negative would make them the same.
jennamil
Cross product has a factor of -1 when the values of the row and column number sum to an odd number, so when you flip it, these all flip.
jiaruiz
v * u = -u * v is because the direction is opposite
I was taught me to remember cross product as:
v x u = det([
i j k
v0 v1 v2
u0 u1 u2
])
I think this is quite helpful.
From the definition of cross product. v x u and u x v are two vectors that have opposite directions. So adding a '-' will let them be the same vector
Swapping operands of the cross product can be seen as switching your fingers when using the right hand rule, so the resulting vectors should oppose each other.
u x v and v x u are two vectors with the same magnitude but opposite directions, by the formal definition of the cross product, thus flipping the direction by making it negative would make them the same.
Cross product has a factor of -1 when the values of the row and column number sum to an odd number, so when you flip it, these all flip.
v * u = -u * v is because the direction is opposite