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

  3. anonymous
    • one year ago
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    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. sohailiftikhar
    • one year ago
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    no they can't

  5. anonymous
    • one year ago
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    Dear sohailiftikhar. How do we prove your statement? P. Radhakrishnamurty

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