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Math Help - Find a Vector

  1. #1
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    Find a Vector

    Find a vector v whose magnitude is 3 and whose component in the i direction is equal to the component in the j direction.

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  2. #2
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    Quote Originally Posted by magentarita View Post
    Find a vector v whose magnitude is 3 and whose component in the i direction is equal to the component in the j direction.
    The vector \vec p = i+j has the magnitude |i+j| = \sqrt{2}

    Therefore the vector \vec u = \frac1{\sqrt{2}} (i+j) has the magnitude 1. (It's a unit vector)

    And therefore the vector \vec v = 3 \cdot \frac1{\sqrt{2}} (i+j) = \left(\frac{3\sqrt{2}}2i + \frac{3\sqrt{2}}2 j  \right)
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  3. #3
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    ok.....

    Quote Originally Posted by earboth View Post
    The vector \vec p = i+j has the magnitude |i+j| = \sqrt{2}

    Therefore the vector \vec u = \frac1{\sqrt{2}} (i+j) has the magnitude 1. (It's a unit vector)

    And therefore the vector \vec v = 3 \cdot \frac1{\sqrt{2}} (i+j) = \left(\frac{3\sqrt{2}}2i + \frac{3\sqrt{2}}2 j \right)
    I did not know about that formula. Great stuff here.

    Thanks
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