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Math Help - Cosine between two vectors

  1. #1
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    Cosine between two vectors

    The question:

    Given the vectors p = (1 1 -1) and q = (2 1 -1), find the cosine between p and q.

    My attempt:

    I found the magnitude of p and q, which are \sqrt{3} and \sqrt{6} respectively.

    I then found the dot product of the vectors, which resulted in 4.

    Using a.b = |a||b|cos\theta I rearranged the equation to:

    cos\theta = \frac{a.b}{|a||b|}

    Substituting the values I got \frac{4}{3\sqrt{2}}

    The answer in the text is \frac{2\sqrt{2}}{6}}

    What am I doing wrong? Thanks!
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  2. #2
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    Quote Originally Posted by Glitch View Post
    The question:

    Given the vectors p = (1 1 -1) and q = (2 1 -1), find the cosine between p and q.

    My attempt:

    I found the magnitude of p and q, which are \sqrt{3} and \sqrt{6} respectively.

    I then found the dot product of the vectors, which resulted in 4.

    Using a.b = |a||b|cos\theta I rearranged the equation to:

    cos\theta = \frac{a.b}{|a||b|}

    Substituting the values I got \frac{4}{3\sqrt{2}}

    The answer in the text is \frac{2\sqrt{2}}{6}}

    What am I doing wrong? Thanks!
    With the given vectors your result is OK, but:

    \frac{4}{3\sqrt{2}} = \frac{4}{3\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{2\sqrt{2}}3
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  3. #3
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    So the text is incorrect?
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