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anonymous

  • 5 years ago

let a and b two vectors such that vector a = 3i + 4j, and the magnitude of vector b = 4, where the angle between the given vectors is 60*. If the vector (m(vector a)+vector b) is perpendicular to vector b, find the value of m.

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  1. amistre64
    • 5 years ago
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    I get it up to the point m(vector a) is m a scalar then?

  2. anonymous
    • 5 years ago
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    yes

  3. amistre64
    • 5 years ago
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    we can just say that Bv is <0,4> right? thats a vecotr of magnitude 4 :)

  4. amistre64
    • 5 years ago
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    no we cant, we have to base it off of A... and 60 degree from it.... back to the draing pad :)

  5. amistre64
    • 5 years ago
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    A<3,4> : ||A|| = 5

  6. anonymous
    • 5 years ago
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    i found that (vector a) dot (vector b)= 10

  7. amistre64
    • 5 years ago
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    by process of the math? or looking at the answers :)

  8. anonymous
    • 5 years ago
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    process of math

  9. amistre64
    • 5 years ago
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    can you type it out so I can see it :) that way I know what we both are looking at.... get me up to speed.

  10. anonymous
    • 5 years ago
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    cos 60= 1/2 1/2= ((vector a) dot (vector b))/(magnitude of vector a * magnitude of vector b) 1/2= ((vector a) dot (vector b))/4*5 1/2= ((vector a) dot (vector b))/20 ((vector a) dot (vector b)) = 10

  11. amistre64
    • 5 years ago
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    to keep things clean; we can use a to mean vector a and b likewise. magnitude is |a| works good. cos(60) = 1/2 1/2 = a*b / |a| |b| 1/2 = a*b / 4*5 1/2 = a*b /20 a*b = 10 ..good work :)

  12. amistre64
    • 5 years ago
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    vectors that are perpendicular have a dot product of zero.

  13. amistre64
    • 5 years ago
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    [m<3,4> + b] * b = 0

  14. amistre64
    • 5 years ago
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    do we know what the vector parts for b are? I was working on that :)

  15. anonymous
    • 5 years ago
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    no we dont

  16. amistre64
    • 5 years ago
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    we can figure it out :) do we need to?

  17. anonymous
    • 5 years ago
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    yeah, i think so,

  18. amistre64
    • 5 years ago
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    heres what I got from what we know.

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  19. amistre64
    • 5 years ago
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    b has 2 options up and to the left, or down and to the right.

  20. amistre64
    • 5 years ago
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    the original angle of "a" is tan-1(4/3) = 53.1301

  21. amistre64
    • 5 years ago
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    b has an angle of either -6.8699 or b has an angle of 113.1301

  22. amistre64
    • 5 years ago
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    4sin(t) will give us the y value and 4cos(t) will give us the x values right?

  23. anonymous
    • 5 years ago
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    yeah

  24. amistre64
    • 5 years ago
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    the left vector option is <-1.57128, 3.67846> for "b" that gives us an angle betwwen them of 60 and a magnitude of 4

  25. amistre64
    • 5 years ago
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    the other option for b is <3.97128, -.47846>

  26. amistre64
    • 5 years ago
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    since we cant move a :) we need to work with these 2 possibilities and see what we get :)

  27. amistre64
    • 5 years ago
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    Do you know if we should include the m in the vector like this? <m3, m4> + < x , y > "b1" ------------ <m3 -1.57128, m4 +3.67846>

  28. anonymous
    • 5 years ago
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    ok i think i can take it from here

  29. amistre64
    • 5 years ago
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    itd a been nice if they had given us a pretty angle to work with off of "a" lol

  30. anonymous
    • 5 years ago
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    yeah i know, vector is very difficult to deal with

  31. amistre64
    • 5 years ago
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    if you got it from here....good luck :)

  32. amistre64
    • 5 years ago
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    you can pick whichever vector for b gets you that 10 ;)

  33. anonymous
    • 5 years ago
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    thank you very much for your help

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