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Math Help - Vector in ai+bj Form

  1. #1
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    Vector in ai+bj Form

    Find a vector determined by the two points in ai+bj form and then find its magnitude.

    (-3,1) and (4,-2)

    (4,7) and (0,5)

    I have no idea where to start. All I know is that a=<1,0> and b=<0,1>

    I think that I want to find the ordered pair/component form of the vector
    1) which will be <7,-3>.

    Do I find the magnitude of that vector? (Squrt(58))

    I do not know what to do know. I get stuck here if the first part is correct and I am not sure if that is correct.

    Thank you
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  2. #2
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    Quote Originally Posted by IDontunderstand View Post
    Find a vector determined by the two points in ai+bj form and then find its magnitude.

    (-3,1) and (4,-2)

    (4,7) and (0,5)

    I have no idea where to start. All I know is that a=<1,0> and b=<0,1>

    I think that I want to find the ordered pair/component form of the vector
    1) which will be <7,-3>.

    Do I find the magnitude of that vector? (Squrt(58))

    I do not know what to do know. I get stuck here if the first part is correct and I am not sure if that is correct.

    Thank you
    Your answer for the first part is correct you just need to sort out the notation.

    <a,b>=a\mathbf{i}+b\mathbf{j} \implies <7,-3>=7\mathbf{i}-3\mathbf{j}
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  3. #3
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    Quote Originally Posted by IDontunderstand View Post
    Find a vector determined by the two points in ai+bj form and then find its magnitude.
    Suppose we have two points: (a,b)~\&~(c,d)
    The vector determined by the two points in ai+bj form is:
    (c-a)\mathbf{i}+(d-b)\mathbf{j}.

    Its magnitude is: \sqrt{(c-a)^2+(d-b)^2}.
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  4. #4
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    So all I have to do is add a i and j after I find the component? My book shows finding a unit vector before it talks about ai+bj form but does not give an example after it.
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  5. #5
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    Quote Originally Posted by IDontunderstand View Post
    So all I have to do is add a i and j after I find the component?
    You also said in your first post "All I know is that a=<1,0> and b=<0,1>". That's part of your confusion- if you write a vector in the form "ai+ bj" is it i that is <1, 0> and j that is < 0,1>, not a and b. a and b are numbers- they are the "components", not the unit vectors.

    My book shows finding a unit vector before it talks about ai+bj form but does not give an example after it.
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