Find two unit vectors orthogonal to both i+j+k and 2i+k.

Question

psymon · Answer

Orthogonal to both would mean cross product I believe.

raffle_snaffle · Answer

I think I know how to find one of the unit vectors...

psymon · Answer

You know how to find the cross product?

raffle_snaffle · Answer

yeah

psymon · Answer

Go for it then :3

raffle_snaffle · Answer

psymon after i use the cross product that is only finding one of the unit vectors orthogonal to the given vectors

theeric · Answer

I agree with Psymon! And remember to find $\large 2$. Don't do all that work and forget that the opposite of your cross-product vector is also orthogonal! I'm sure people do that all the time.

psymon · Answer

@theEric just answered your question :P

raffle_snaffle · Answer

Haha wow...

raffle_snaffle · Answer

Thanks theric.=)

theeric · Answer

You're welcome! :)

So, speaking in general terms, $\vec a\times\vec b=\vec c$, and you could also do $\vec b\times\vec a=\vec d$. Well, if you can imagine, $\vec c=-\vec d$, so you don't have to use the cross product twice (although that will get you the two orthogonal vectors). It might just make sense that the opposite of the cross-product vector is also orthogonal.

raffle_snaffle · Answer

so it look something like this...

raffle_snaffle · Answer

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