anonymous
  • anonymous
Do two 2-D vectors that are not mutually perpendicular, constitute a pair of linearly independent vectors?
Physics
chestercat
  • chestercat
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IrishBoy123
  • 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
IrishBoy123
  • IrishBoy123
oops longer example here https://gyazo.com/58587800e65fda229fbac26f34289a0a url appears in screengrab
anonymous
  • 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

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sohailiftikhar
  • sohailiftikhar
no they can't
anonymous
  • anonymous
Dear sohailiftikhar. How do we prove your statement? P. Radhakrishnamurty

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