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Math Help - Components

  1. #1
    Junior Member NAPA55's Avatar
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    Components

    Quick question- if I know the magnitude of a certain vector, the coordinates of its tail (as an ordered triple), and that the vector itself is going in the same direction as another vector (given x/y/z coordinates of the other one), how can I find the components of the vector itself?

    I got an answer but I don't think it's right because I can swap my values between x/y/z for it to work... but isn't there just 1 answer (only 1 possible x, y, and z component)?
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  2. #2
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    Quote Originally Posted by NAPA55 View Post
    Quick question- if I know the magnitude of a certain vector, the coordinates of its tail (as an ordered triple), and that the vector itself is going in the same direction as another vector (given x/y/z coordinates of the other one), how can I find the components of the vector itself?

    I got an answer but I don't think it's right because I can swap my values between x/y/z for it to work... but isn't there just 1 answer (only 1 possible x, y, and z component)?
    Hello,

    What do you call "same direction" ? Do you have a given example so that it'd be easier to help you ?
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  3. #3
    Junior Member NAPA55's Avatar
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    I'll just make something up, so when I do the actual problems I still have to think lol

    - They give the coordinates of the tail
    - They give the magnitude
    - They say the vector is in the same direction as u = (4, -3, -6)

    I guess by direction they mean which way it is is moving (on positive or negative axis)...

    From my made up question here, x is a positive direction while y and z are negative, so I guess that means that the vector that I'm finding has to have a positive x value but negative y and z values.
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  4. #4
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    Quote Originally Posted by NAPA55 View Post
    I'll just make something up, so when I do the actual problems I still have to think lol

    - They give the coordinates of the tail
    - They give the magnitude
    - They say the vector is in the same direction as u = (4, -3, -6)

    I guess by direction they mean which way it is is moving (on positive or negative axis)...

    From my made up question here, x is a positive direction while y and z are negative, so I guess that means that the vector that I'm finding has to have a positive x value but negative y and z values.
    Because I'm boring lets use the tail at (a,b,c)

    So a vector with the same direction as (4,,-3,-6) passing through (a,b,c) can be written as

    v=(a,b,c)+t(4,-3,-6)=(4t+a,-3t+b,-6t+c)


    We can find the magnitude

    \sqrt{(4t+a)^2+(-3t+b)^2+(-6t+c)^2}=M

    From here plug in the magnitude for M and solve the quadratic for the value of t and sub back into the original equation.

    Good luck.
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  5. #5
    Junior Member NAPA55's Avatar
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    Wouldn't that give 2 values for t, and therefore 2 possible vectors?

    I think there's only supposed to be 1 answer.
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    Quote Originally Posted by NAPA55 View Post
    Wouldn't that give 2 values for t, and therefore 2 possible vectors?

    I think there's only supposed to be 1 answer.
    I hope this helps.

    A vector with magnitude 5 and its tail at (0,0) in the direction (3,4)

    well one possible answer would be the vector 3i +4j, but what is wrong with
    -3i-4j these both have the same magnitude, but face the opposite way.

    I guess it depends on how they define direction, you may just want to pick the positive one.
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  7. #7
    Junior Member NAPA55's Avatar
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    I did it another way. Does this work?

    I took the vector given (the one that mine follows in the same direction). Then I converted it to a unit vector with magnitude 1. I multiplied the unit vector by a scalar of the magnitude given to come up with a new vector.

    Then I separated that new vector into components.

    Are the components I'm looking for:
    a) The x, y, and z values when the vector has the tail at the origin?

    or

    b) The x, y, and z values of the tip?

    I think the tail information is irrelevant.
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