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Math Help - beginner problem linear algebra

  1. #1
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    beginner problem linear algebra



    Not sure how to do this one, can I get some tips? Thanks.
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  2. #2
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    Try using cos{\theta}=\frac{u\cdot v}{||u|| \;\ ||v||}

    If you get 1, then cos^{-1}(1)=0. That means there is no angle between them and they are parallel.

    u\cdot v is the dot product of u and v.

    i.e. u\cdot v=([-6,3,3],[-4,2,2])=36

    ||u|| \;\ ||v||=\sqrt{(-6)^{2}+3^{2}+3^{2}}\sqrt{(-4)^{2}+2^{2}+2^{2}}=36

    cos{\theta}=\frac{36}{36}=1

    cos^{-1}(1)=0

    Parallel.
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  3. #3
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    I think it is much simpler than that, we haven't covered any of that material you mentioned. We've only covered topics to do with vectors. I think it has something to do with scalar multiples maybe?
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  4. #4
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    Here is the criteria: u1 ans u2 are parallel if their co-ordinates are in the same proportion. so u1 and u3 are parallel: -6/-4 = 3/2 = 3/2.

    so u1 = k x u3 hence parallel. To check if the direction is same check the sign of k
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