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Thread: Vectors

  1. #1
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    Vectors



    sry i but i really have no idea how to start the question... i have problems with both parts of the question as they are similar...

    i am not asking u to spoonfeed me, perhaps u can solve the first part and let me solve the second part as they are similar ^^

    thanks in advance
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  2. #2
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    Shift y from the present position to (2,1) and (4,3).

    Complete the parallelogram. The resultant of x and y will be (1,4) and (4,3)

    Parallel to this resultant from P is (0,5) and (3,4)
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  3. #3
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    thanks! mind if i ask u for part ii how do i handle the fraction?
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  4. #4
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    Quote Originally Posted by Punch View Post
    thanks! mind if i ask u for part ii how do i handle the fraction?
    3y/2 will be (4, 1) and (7, 4)

    Shift x to the right so that x touches y.
    Last edited by sa-ri-ga-ma; Jun 7th 2010 at 10:23 PM.
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  5. #5
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    Movement (displacement) vectors

    Hello Punch

    From the diagram, we can see that $\displaystyle \textbf{x}$ represents a movement which can be described as:
    Move 1 unit to the right and 3 units down.
    We can write this as
    $\displaystyle \textbf{x}=\binom{1}{-3}$
    Similarly $\displaystyle \text{y}$ represents the movement:
    Move 2 units to the right and 2 units up
    or:
    $\displaystyle \textbf{y}=\binom{2}{2}$
    We add two movement (or displacement) vectors together using an ordinary $\displaystyle +$ sign, by thinking of $\displaystyle +$ as representing the phrase 'and then'. So $\displaystyle \textbf{x} + \textbf{y}$ means
    Move 1 unit to the right and 3 units down
    and then
    Move 2 units to the right and 2 units up
    which is obviously equivalent to
    Move 3 units to the right and 1 unit down
    We sometimes write all of this as:
    $\displaystyle \textbf{x} + \textbf{y}=\binom{1}{-3} + \binom{2}{2}$
    $\displaystyle = \binom{3}{-1}$
    Do you see how it works?

    Now $\displaystyle \vec{PR}$ stands for:
    Move from $\displaystyle P$ to $\displaystyle R$
    So if $\displaystyle \vec{PR}=\textbf{x} + \textbf{y}$ and we must start at the point $\displaystyle P\; (0,5)$, and carry out the movement $\displaystyle \binom{3}{-1}$. When we do this, we get to the point $\displaystyle (3,4)$. So that's where $\displaystyle R$ is: $\displaystyle (3,4)$.

    Now $\displaystyle \frac32\textbf{y}$ is the same movement as $\displaystyle \textbf y$, but multiplied by $\displaystyle \frac32$. In other words:
    $\displaystyle \frac32\textbf{y}=\frac32\times\binom22$
    $\displaystyle =\binom33$
    So:
    $\displaystyle \frac32\textbf{y}-\textbf x=\binom33 - \binom{1}{-3}$
    $\displaystyle =\binom{2}{6}$ (Check this carefully!)
    and this is the movement $\displaystyle \vec{AB}$. So, to find the position of the point $\displaystyle B$, start at $\displaystyle A$ and carry out the movement $\displaystyle \binom26$. Can you see that $\displaystyle B$ is at $\displaystyle (6,6)$?

    Grandad
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  6. #6
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    HEY Grandad !!! Many THX !!!!!!!!!!! your workings are excellent as usual, i fully understood them and have never heard about this method before!!!!!!!!!!!!!!!!
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