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    IBMediumVectors10–12

    Vector Dot Product

    Produto Escalar de Vetores

    Given vectors \vec{a} = (3, -1, 2) and \vec{b} = (1, 4, -3), find: a) The dot product \vec{a} \cdot \vec{b} b) The angle between \vec{a} and \vec{b} (to the nearest degree).

    \vec{a} \cdot \vec{b} = a_1b_1 + a_2b_2 + a_3b_3. For the angle, use \cos \theta = \frac{\vec{a} \cdot \vec{b}}{|\vec{a}| \cdot |\vec{b}|}.

    Solution

    Step 1 of 5

    1. 1.a) \vec{a} \cdot \vec{b} = 3(1) + (-1)(4) + 2(-3) = 3 - 4 - 6 = -7