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Math Help - Help with checking Vector Question

  1. #1
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    Help with checking Vector Question

    Hey guys I am not sure if i am on the right track here so i need some advice

    Question is:

    if \vec{a}=3i-2j , \vec{b}=-4i+4j , and \vec{c}=6i+-9j express the following vectors in their simplest form:

    (i) -5\vec{b}
    (ii) 2\vec{a}-\frac{1}{2}\vec{c}
    (iii) \frac{2}{3}\vec{a}-\frac{1}{2}\vec{b}-\frac{1}{4}\vec{c}

    My Solution:

    (i) -5\left(-4i+4j \right)=20i+\left(-20j \right)
    (ii) 2(3i-2j)-\frac{1}{2}(6i+(-9)j)
    = 6i-4j-3i+(-\frac{9}{2})j
    = (6-3=3i) -4j-\frac{9}{2}
    = -\frac{4}{1}-\frac{9}{2}
    =-\frac{8}{2}-\frac{9}{2}
    =-\frac{17}{2}

    Answer? 3i-\frac{17}{2}j

    (iii) \frac{2}{3}(3i-2j)-\frac{1}{2}(-4i+4j)-\frac{1}{4}(6i+(-9)j)
    (2i-\frac{4}{3}j)-(-2i+2j)-(\frac{3}{2}i+(-\frac{9}{4}j)
    2i+2i-\frac{3}{2}i
    = \frac{4}{1}i+\frac{3}{2}i
    = \frac{8}{2}+\frac{3}{2}
    =\frac{11}{2}i

    -\frac{4}{3}j+\frac{2}{1}j-\frac{9}{4}j
    = -\frac{16}{12}j+\frac{24}{12}j-\frac{27}{12}j
    = -\frac{19}{12}j

    Answer? \frac{11}{2}i-\frac{19}{12}j
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  2. #2
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    while removing the brackets, you have to follow the following rule.

    -2(a-b) = -2a + 2b

    -2(a+b) = -2a - 2b

    Therefore your second the third problems are wrong. Correct it.
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  3. #3
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    Quote Originally Posted by sa-ri-ga-ma View Post
    while removing the brackets, you have to follow the following rule.

    -2(a-b) = -2a + 2b

    -2(a+b) = -2a - 2b

    Therefore your second the third problems are wrong. Correct it.
    ok so (ii) answer is <br />
3{\bf i}+(-4+\frac{9}{2}){\bf j}=3{\bf i}+\frac{1}{2}{\bf j}<br />

    now i will do the (iii) one again
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  4. #4
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    Ok would the (iii) one be

    \frac{5}{2}i+\frac{7}{6}j
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  5. #5
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    Hello, mathematicallyretarded!

    You are making hard work out of it.

    This is basically Algebra I . . . combining like terms.


    Given: . \begin{array}{ccc}\vec a &=&3i-2j \\ \vec b &=&-4i+4j \\ \vec c &=&6i-9j\end{array}

    Express the following vectors in their simplest form:

    (i) \;-5\vec{b}

    -5\vec b \;\;=\;\;-5(-4i + 4j) \;\;=\;\;20i - 20j



    (ii) \;\;2\vec a -\tfrac{1}{2}\vec c

    2\vec a - \tfrac{1}{2}\vec c \;\;=\;\;2(3i - 2j) - \tfrac{1}{2}(6i-9j)

    . . . . . . =\;\;6i - 4j - 3i + \tfrac{9}{2}j

    . . . . . . =\;\;3i + \frac{1}{2}j



    (iii)\;\;\tfrac{2}{3}\vec a -\tfrac{1}{2}\vec b - \tfrac{1}{4}\vec c

    \tfrac{2}{3}\vec a - \tfrac{1}{2}\vec b - \tfrac{1}{4}\vec c \;\;=\;\;\tfrac{2}{3}(3i - 2j) - \tfrac{1}{2}(-4i + 4j) - \tfrac{1}{4}(6i - 9j)

    . . . . . . . . . =\;\;2i - \tfrac{4}{3}j + 2i - 2j - \tfrac{3}{2}i + \tfrac{9}{4}j

    . . . . . . . . . =\;\;\frac{5}{2}i - \frac{13}{12}j

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  6. #6
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    Thanks! I have to learn to keep it simple
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