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I believe so, yes...

yes yes yes.

And so, if they do not span \(\Re^3\), they are linearly dependent, right?

yeah three vectors that aren't all linearly independent cannot span \[\mathbb R^3\]

i wouldn't word it like that

thats is better yes

That's pretty nice :) Thanks!
May I ask one more question about linear dependence here?

sure

\(\vec{v}\) **

if you find the angle between vectors is π/2 the vectors will be independent

How to find the angle between three vectors??

\[\theta=\arccos\left(\frac{\vec u \cdot \vec v}{||\vec u||~~||\vec v||}\right)\]

For multiple vectors you would have to find the angle between each possible pair of vectors

For the case of two vectors, I still can do it. But not for three or more vectors..