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Math Help - Vectors and an angle

  1. #1
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    Vectors and an angle

    "Suppose a and b are vectors such that |a| = 3, b = 2 and the angle between a and b is (theta) = pi/3. Evaluate (a + b) . (a and b)." (Note: The '.' implying dot-product).

    I am unsure with how to approach this question, considering there is also an angle involved. I am moreover unsure with how to evaluate the equation, since there are no numbers within it and it is with using the dot product. I did at first try expanding out the equation but then realised that was wrong. I really do not know what the angle implies in this question, either.
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  2. #2
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    Quote Originally Posted by cottontails View Post
    "Suppose a and b are vectors such that |a| = 3, b = 2 and the angle between a and b is (theta) = pi/3. Evaluate (a + b) . (a and b)." (Note: The '.' implying dot-product).

    I am unsure with how to approach this question, considering there is also an angle involved. I am moreover unsure with how to evaluate the equation, since there are no numbers within it and it is with using the dot product. I did at first try expanding out the equation but then realised that was wrong. I really do not know what the angle implies in this question, either.
    I mentioned in your post about projections the geometric defintion of the dot product that is

    \mathbf{a}\cdot \mathbf{b}=||\mathbf{a}||||\mathbf{b}||\cos(\theta  )

    Where theta is the angle between two vectors.

    Now what you did first is correct you must also remember \mathbf{a}\cdot \mathbf{a}=||a||^2

    Use the distributive property of the dot product.
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  3. #3
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    Quote Originally Posted by cottontails View Post
    "Suppose a and b are vectors such that |a| = 3, b = 2 and the angle between a and b is (theta) = pi/3. Evaluate (a + b) . (a and b)." (Note: The '.' implying dot-product).
    What do you mean by "a and b"?

    I am unsure with how to approach this question, considering there is also an angle involved. I am moreover unsure with how to evaluate the equation, since there are no numbers within it and it is with using the dot product. I did at first try expanding out the equation but then realised that was wrong. I really do not know what the angle implies in this question, either.
    Follow Math Help Forum on Facebook and Google+

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