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Math Help - Vector Question

  1. #1
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    Vector Question

    For any vectors v and w, consider the following function of scalar t:
    q(t)=(v+t w) dot (v+ t w).
    (1) Explain why q(t) is greater than or equal to 0 for all real t.
    (2) Expand q(t) as quadratic polynomial in t using the dot product properties.
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  2. #2
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    Quote Originally Posted by vvc531 View Post
    For any vectors v and w, consider the following function of scalar t:
    q(t)=(v+t w) dot (v+ t w).
    (1) Explain why q(t) is greater than or equal to 0 for all real t.
    (2) Expand q(t) as quadratic polynomial in t using the dot product properties.
    Should this look like this?

    q(t)=<v+t,w>\cdot<v+t,w>
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