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anonymous

  • one year ago

Can someone help me with some math questions? I'll fan and medal. :)

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  1. anonymous
    • one year ago
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  2. hartnn
    • one year ago
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    do you know how to get projection of one vector on other? tried to solve this?

  3. hartnn
    • one year ago
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    Projection of vector a on vector b is \(\LARGE \dfrac{a.b}{|b|}\)

  4. anonymous
    • one year ago
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    So it would start off like this?.... (1.6i + 3.3j) (-2.1i -0.5j) = -3.36 -6.93 -1.65 -0.8

  5. hartnn
    • one year ago
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    note that \(i . j \) and \(j.i\) both = 0 as they are perpendicular vectors!

  6. hartnn
    • one year ago
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    so you'll only have 1.6*(-2.1) + 3.3*(-0.5) = ...

  7. anonymous
    • one year ago
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    So just to be clear - Whenever you're multiplying the different variables in a vector, the become zero?

  8. hartnn
    • one year ago
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    correction* whenever you're taking the dot product of perpendicular vectors, the product = 0 i , j and k are perpendicular vecotrs

  9. anonymous
    • one year ago
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    Got it. So... 1.6*(-2.1) + 3.3*(-0.5) = -3.36i -1.65j then you divide that answer by (-2.1i -0.5j) (-3.36i -1.65j) / (-2.1i -0.5j) =...

  10. anonymous
    • one year ago
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    Give me just a second on the division. I think I did something wrong.

  11. hartnn
    • one year ago
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    so your u.v will be = 1.6*(-2.1) + 3.3*(-0.5) = ... its a numeric value, because its a dot product it won't have i's and j's in it!

  12. hartnn
    • one year ago
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    and for the denominator its magnitude of v = \(\sqrt {2.1^2+0.5^2} = .. \) there is no need of doing complex divisions :)

  13. hartnn
    • one year ago
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    1.6*(-2.1) + 3.3*(-0.5) = -5.01

  14. anonymous
    • one year ago
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    So the numerator is -5.01 and the denominator is about 2.16 and you would divide that?

  15. hartnn
    • one year ago
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    thats right that will give you the magnitude of the projection vector :)

  16. anonymous
    • one year ago
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    About -2.32

  17. hartnn
    • one year ago
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    thats the magnitude, now you only need the direction of projection vector and since projection is along the vector 'v' its direction will be same as that of vector v !

  18. hartnn
    • one year ago
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    for that, you'll need to find the unit vector in the direction of v and then mutiply the above answer to it.

  19. anonymous
    • one year ago
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    Wouldn't "b" be the direction? (-2.1i -0.5j)

  20. hartnn
    • one year ago
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    you need projection of vector u along vector 'v' so its direction will be along vector 'v' whats b and where it came form ?

  21. hartnn
    • one year ago
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    unit vector along v = v/ |v| and we already know |v| = 2.16

  22. hartnn
    • one year ago
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    so unit vector along v = (-2.1i -0.5j)/ 2.16 and your projection will be -2.32 times the above answer

  23. anonymous
    • one year ago
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    (-2.1i -0.5j)/ 2.16 Would that be (-0.97i -0.23)?

  24. hartnn
    • one year ago
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    what do u get after multiplying that with -2.32?

  25. anonymous
    • one year ago
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    -2.32 (-0.97i -0.23) = (-2.25i -0.53j)

  26. hartnn
    • one year ago
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    two negatives become positive! and you can approximate 2.25 to 2.3 and 0.53 to 0.5 :)

  27. hartnn
    • one year ago
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    -2.32 * -0.97 = +2.3 -2.32 * -0.23 = +0.5

  28. anonymous
    • one year ago
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    Oops! I didn't even see the double negatives. Thank you for catching that. So the answer would be B. (2.3i +0.5j)

  29. hartnn
    • one year ago
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    yes, correct! good work :)

  30. anonymous
    • one year ago
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    Thank you for your help. :)

  31. hartnn
    • one year ago
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    most welcome ^_^

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