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Math Help - Vectors

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    Vectors

    What would I need to do to approximate the angle between the two vectors 4i-3j and 4i+3j.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by gretchen View Post
    What would I need to do to approximate the angle between the two vectors 4i-3j and 4i+3j.
    we will use the formula for the dot product, i hope you know what the dot product is:

    we have:

    cos(x) = a*b/(|a||b|)

    where * means dot product and x is the angle between the two (nonzero) vectors:

    a*b = <4,-3>*<4,3> = 4*4 + (-3)*3 = 16 - 9 = 7

    |a| = sqrt(4^2 + (-3)^2) = sqrt(25) = 5
    |b| = sqrt(4^2 + 3^2) = sqrt(25) = 5

    => cos(x) = 7/(5)(5) = 7/25
    => x = cos^-1(7/25)
    => x = 1.287 radians
    or x = 73.74 degrees
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  3. #3
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    Quote Originally Posted by gretchen View Post
    What would I need to do to approximate the angle between the two vectors 4i-3j and 4i+3j.
    Hello, gretchen,

    1. draw a sketch (see attachment).
    2. both vectors have the same length (l = 5) thus you deal with the legs of an isosceles triangle.
    3. use half of the isosceles triangle: It is a right triangle.
    4. now you can calculate the angle by:

    2*arctan(3/4) = 73.74

    EB
    Attached Thumbnails Attached Thumbnails Vectors-winkl_vectgretchen.gif  
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