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Math Help - Vector addition, components

  1. #1
    Member nautica17's Avatar
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    Vector addition, components

    This is a problem from my calculus 3 class.

    "Find the component forms of v + w and v - w in 2-space, given that ||v|| = 1, ||w|| = 1, v makes an angle of pi/6 with the positive x-axis, and w makes an angle of 3pi/4 with the positive x-axis."

    Okay, so I think have the answer but I want to be a hundred percent certain.

    Looking at the unit circle.. I get these values for the components based on the angles given.
    v = <sqrt(3)/2, 1/2>
    w = <-sqrt(2)/2, sqrt(2)/2>

    And so...
    v + w = < ( sqrt(3)/2 + (-sqrt(2)/2) ), ( 1/2 + sqrt(2)/2 ) >
    = < ( (sqrt(3) - sqrt(2)) / 2 ), ( (1 + sqrt(2)) / 2 ) >

    v - w = < ( sqrt(3)/2 - (-sqrt(2)/2) ), ( 1/2 - sqrt(2)/2 ) >
    = < ( (sqrt(3) + sqrt(2)) / 2 ), ( (1 - sqrt(2)) / 2 ) >

    Am I doing it right?
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  2. #2
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    Quote Originally Posted by nautica17 View Post
    "Find the component forms of v + w and v - w in 2-space, given that ||v|| = 1, ||w|| = 1, v makes an angle of pi/6 with the positive x-axis, and w makes an angle of 3pi/4 with the positive x-axis."
    v = <sqrt(3)/2, 1/2>
    w = <-sqrt(2)/2, sqrt(2)/2>
    And so...
    v + w = < ( sqrt(3)/2 + (-sqrt(2)/2) ), ( 1/2 + sqrt(2)/2 ) >
    = < ( (sqrt(3) - sqrt(2)) / 2 ), ( (1 + sqrt(2)) / 2 ) >

    v - w = < ( sqrt(3)/2 - (-sqrt(2)/2) ), ( 1/2 - sqrt(2)/2 ) >
    = < ( (sqrt(3) + sqrt(2)) / 2 ), ( (1 - sqrt(2)) / 2 ) >
    Am I doing it right?
    Yes you are.
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  3. #3
    Member nautica17's Avatar
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    Cool, thanks!
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