- #1

ChiralSuperfields

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- Homework Statement
- I am trying to derive the formula ##\vec {u} \times \vec {v} = (u_2v_3 - u_3v_2)\hat i + (u_3v_1 - u_1v_3)\hat j + (u_1v_2 - u_2v_1)\hat k ## because it is extremely difficult to commit to memory for my upcoming exam

- Relevant Equations
- ##\vec {u} \times \vec {v} = (u_2v_3 - u_3v_2)\hat i + (u_3v_1 - u_1v_3)\hat j + (u_1v_2 - u_2v_1)\hat k ##

So far, I have got the equations,

##u \cdot (\vec u \times \vec v) = 0##

##u_1a + u_2b + u_3c = 0##

##v_1a + v_2b + v_3c = 0##

Could some please give me some guidance?

Many thanks!

##u \cdot (\vec u \times \vec v) = 0##

##u_1a + u_2b + u_3c = 0##

##v_1a + v_2b + v_3c = 0##

Could some please give me some guidance?

Many thanks!