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Math Help - Gr 12. Vector problem!

  1. #1
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    Gr 12. Vector problem!

    Given a and b unit vectors.
    a) if the angle between them is 60deg, calculate (6a + b) dot (a - 2b)
    b) if |a + b| = root 3, determine (2a - 5b) dot (b + 3a)
    a and b are unit vectors

    Please and thank you!
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  2. #2
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    Quote Originally Posted by narutoblaze View Post
    Given a and b unit vectors.
    a) if the angle between them is 60deg, calculate (6a + b) dot (a - 2b)
    b) if |a + b| = root 3, determine (2a - 5b) dot (b + 3a)
    a and b are unit vectors

    Please and thank you!

    Dont forget that the dot product is a LINEAR.

    (\vec a + \vec b) \cdot \vec c =\vec a \cdot \vec c +\vec b \cdot \vec c for all vectors in you space and

    for any real number  \alpha,\beta \in \mathbb{R}
    (\alpha \vec a) \cdot (\beta \vec b)=\alpha \beta (\vec a \cdot \vec b)

    Also the defintion \vec a \cdot \vec b= ||a||||b||\cos(\theta)

    using these two properties we get

    (2\vec a-5 \vec b) \cdot (\vec b+\vec 3a) =(2\vec a)\cdot (\vec b+\vec 3a)+(-5\vec b)\cdot (\vec b+\vec 3a)=

    (2\vec a)\cdot (\vec b)+(2\vec a)\cdot (3\vec a)+(-5\vec b)\cdot (\vec b)+(-5\vec b)\cdot (\vec 3a)=

    2(\vec a \cdot \vec b)+6(\vec a \cdot \vec a)-5(\vec b \cdot \vec b)-15 (\vec b \cdot \vec a)

    Since a and be are both unit vectors we get

     <br />
2\cos(60)+6\cos(0)-5\cos(0)-15\cos(60)<br /> <br />
    Just simplify from here
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