Let v = 8j and let u be a vector with length 9 that starts at the origin and rotates in the xy-plane. Find the maximum and minimum values of

Question

Let v = 8j and let u be a vector with length 9 that starts at the origin and rotates in the xy-plane. Find the maximum and minimum values of the length of the vector u × v.

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Trúc Chi 1 month 2021-08-15T21:19:34+00:00 1 Answers 0 views 0

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    2021-08-15T21:20:47+00:00

    Answer:

    |u\times v|_{min}=0

    |u\times v|_{max}=72

    Step-by-step explanation:

    We are given that

    v=8 j

    |u|=9

    Let u=ai+bj

    We have to find the maximum and minimum values of the length of the vector

    u × v.

    u\times v=\begin{vmatrix}i&j&k\\a&b&0\\0&8&0\end{vmatrix}=8ak

    |u\times v|=\sqrt{(8a)^2}=\sqrt{64a^2}

    |u|=\sqrt{a^2+b^2}=9

    a^2+b^2=81

    The minimum value of a^2=0

    Then, |u\times v|_{min}=0

    Maximum value of  a^2=81

    |u\times v|_{max}=\sqrt{64(81)}=72

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