## anonymous one year ago Do two 2-D vectors that are not mutually perpendicular, constitute a pair of linearly independent vectors?

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1. IrishBoy123

https://gyazo.com/2b28c690ecdbb50476c734cfb981c183 in brief, yes, unless they are parallel. if they are parallel $$\vec u\times \vec v = 0$$ so $\left|\left|\begin{matrix}u_x & u_y \\ v_x & v_y\end{matrix}\right|\right| = 0$ as in this longer example: https://gyazo.com/a260ae04000052418719fb02795c2bf8

2. IrishBoy123

oops longer example here https://gyazo.com/58587800e65fda229fbac26f34289a0a url appears in screengrab

3. anonymous

Thank you IrishBoy123. But I want you to take just one pair of two 2_D vectors that are non ortogonal and show the proof. You have taken a set of 3-D vectors. I am not interested in that. I am interested only in the case where all the vectors are in one plane only. Only this case would be useful to me. P. Radhakrishnamurty

4. anonymous

no they can't

5. anonymous