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anonymous

  • 4 years ago

Find the area of the parallelogram with the defining vectors i) a=( 4,-5) and b= (7,2) ii) a= (4,-5,3) and b= (7,2,-4)

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  1. amistre64
    • 4 years ago
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    subtract one vector from the other to get it to the origin; is my first thought

  2. amistre64
    • 4 years ago
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    but my first thought aint always too good :)

  3. amistre64
    • 4 years ago
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    |dw:1327355180731:dw|

  4. amistre64
    • 4 years ago
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    maybe better idea. magnitude of b * height; where height is the "a"sin(a)

  5. amistre64
    • 4 years ago
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    the determinate of the vector matrix of the first one would be good, but not work out to well for the second

  6. amistre64
    • 4 years ago
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    i can recall the dot product stuff for cos(t) but never for sin(t) for some reason

  7. anonymous
    • 4 years ago
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    Thank you!!

  8. amistre64
    • 4 years ago
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    The cross product a × b is defined as a vector c that is perpendicular to both a and b, with a direction given by the right-hand rule and a magnitude equal to the area of the parallelogram that the vectors span. from the wiki i think

  9. amistre64
    • 4 years ago
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    so |axb| seems to be the area of the parallelogram if im reading this right

  10. amistre64
    • 4 years ago
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    now i gotta recall how to cross a 2component vector

  11. amistre64
    • 4 years ago
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    3 components i can do :)

  12. amistre64
    • 4 years ago
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    ii) a= (4 -5 3) and b= (7 2 -4) --------------- x = 20-6 = 14 y=-(-16-21) = 37 z = 8+35 = 43 sqre them add them and sqrt them for magnitude; might wanna use a calcultor :)

  13. amistre64
    • 4 years ago
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    http://www.wolframalpha.com/input/?i=sqrt%2814%5E2%2B37%5E2%2B43%5E2%29 58.5 thereabouts?

  14. amistre64
    • 4 years ago
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    cross was good; i can wolf the other one for simplicities sake too

  15. amistre64
    • 4 years ago
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    determinant of the vector matrix on 1 is 43, with any luck i recalled that stuff right

  16. anonymous
    • 4 years ago
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    woowww thank you soo soo much!! :)

  17. amistre64
    • 4 years ago
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    do we know if i was right? lol

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