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Math Help - Vectors

  1. #1
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    Vectors

    Hello all, i need some help with these questions. I didn't have any clue on how to approach these so an explanation would be appreciated.

    1.) O, A and B are the points (0,0), (3,4) and (4,-6) respectively.

    a.) C is the point such that OA = OC + OB. Find the coordinates of C

    b.) D is the point (1,24) and OD = hOA + kOB. Find the values of h and k.

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    2.) If a = 5i - sj + 2k and b = ti + 2j + uk are equal vectors, find

    a.) i.) s
    ii.) t
    iii.) u
    iv.) Magnitude of a

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  2. #2
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    Quote Originally Posted by andrew2322 View Post
    Hello all, i need some help with these questions. I didn't have any clue on how to approach these so an explanation would be appreciated.

    1.) O, A and B are the points (0,0), (3,4) and (4,-6) respectively.

    a.) C is the point such that OA = OC + OB. Find the coordinates of C

    b.) D is the point (1,24) and OD = hOA + kOB. Find the values of h and k.

    [snip]
    a.) OA = <3, 4> and OB = <4, -6>. Let C have coordinates (x, y). Then OC = <x, y>.

    Therefore <3, 4> = <x, y> + <4, -6> = <x + 4, y - 6>.

    Therefore 3 = x + 4 and 4 = y - 6 ....

    b.) OD = <1, 24>.

    Therefore <1, 24> = h <3, 4> + k <4, -6> = <3h + 4k, 4h - 6k>

    Therefore:

    1 = 3h + 4k .... (1)

    24 = 4h - 6k .... (2)

    Solve equations (1) and (2) simultaneously.
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  3. #3
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    Quote Originally Posted by andrew2322 View Post
    [snip]

    2.) If a = 5i - sj + 2k and b = ti + 2j + uk are equal vectors, find

    a.) i.) s
    ii.) t
    iii.) u
    iv.) Magnitude of a

    [snip]
    i.) If a = b then the components are equal: -s = 2 => s = -2.

    Same idea for ii.) and iii.)

    iv.) a = 5i + 2j + 2k. Use the usual formula for getting the magnitude of a vector.
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    thanks

    thanks for replying to those questions, i still have a few question though :P

    1.) In question 1, why is it that the sum of the coordinates must equal to the coordinates of OA?

    2.) And with question two, if two vectors are equal, does that mean that they're the same vector?
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  5. #5
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    Quote Originally Posted by andrew2322 View Post
    thanks for replying to those questions, i still have a few question though :P

    1.) In question 1, why is it that the sum of the coordinates must equal to the coordinates of OA? Mr F says: OA = OB + OC ...... Have you been taught how to add vectors together (OB + OC in this case) and that the result of this addition is another vector? And when two vectors are equal their components are equal.

    2.) And with question two, if two vectors are equal, does that mean that they're the same vector?
    Mr F says: It means that they have the same components. They have the same magnitude and the same direction.
    Some of your trouble probably arises from not understanding how to add vectors and what it means when two vectors are equal. I suggest you extensively revise these things.
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  6. #6
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    hey

    hey, can't they have different components but still have the same magnitude and direction?
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  7. #7
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    Quote Originally Posted by andrew2322 View Post
    hey, can't they have different components but still have the same magnitude and direction?
    No!
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