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Math Help - vectors in 2D space again

  1. #1
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    vectors in 2D space again

    question: With respect to an origin, O, the points A, B and C have position vectors (2i+5j)m, (-i+2j)m and (7i+15j)m respectively.
    (a) Express vector BA, in terms of i and j.
    (b) Given that P is the point on BA, between B and A, such that BP/PA =1/2
    Write down vector BP, in terms of i and j
    (c) Hence, or otherwise, find vector OP, in terms of i and j.

    my ans:
    (a) -3m(i+j)
    (b) -m(i+j)
    (c) 3mj
    book's ans:
    (a) 3i+3j
    (b) i+j
    (c) 3j

    i have no idea where all the 'm' goes
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by afeasfaerw23231233 View Post
    question: With respect to an origin, O, the points A, B and C have position vectors (2i+5j)m, (-i+2j)m and (7i+15j)m respectively.
    (a) Express vector BA, in terms of i and j.
    (b) Given that P is the point on BA, between B and A, such that BP/PA =1/2
    Write down vector BP, in terms of i and j
    (c) Hence, or otherwise, find vector OP, in terms of i and j.

    my ans:
    (a) -3m(i+j)
    (b) -m(i+j)
    (c) 3mj
    book's ans:
    (a) 3i+3j
    (b) i+j
    (c) 3j

    i have no idea where all the 'm' goes
    The "m" is probably just a distance unit: a meter.

    You have the correct answers for a) and b), the book didn't print (I presume) the negative sign.

    -Dan
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  3. #3
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    oops, thanks!
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  4. #4
    MHF Contributor red_dog's Avatar
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    I think your answers are not just right.
    We have:

    \overrightarrow{OA}=2\overrightarrow{i}+5\overrigh  tarrow{j}, \ \overrightarrow{OB}=-\overrightarrow{i}+2\overrightarrow{j}

    Then \overrightarrow{BA}=\overrightarrow{OA}-\overrightarrow{OB}=2\overrightarrow{i}+5\overrigh  tarrow{j}+\overrightarrow{i}-2\overrightarrow{j}=3\overrightarrow{i}+3\overrigh  tarrow{j}

    And b) is also wrong.
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