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30 November, 13:47

Consider the vector v = (-7,8). What is the angle between v = (-7,8) and the positive x-axis? Part 1: Use the formula v1 x v2=|v1||v2|cos theta to find the cosine of the angle between the two vectors (-7,8) and (1,0).

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  1. 30 November, 13:50
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    (1) To find the angle between v and positive x-axis, we first determine the angle formed by v and the negative x-axis. Since v = (-7,8), its vertical measure y is 8 units and horizontal measure x is 7 units.

    arctan (8/7) = 48.81°

    Solving for angle between v and positive x-axis:

    180° - 48.81° = 131.19°

    (2) v1 x v2=|v1||v2|cosθ

    Calculating for the dot product of the vector:

    v1 x v2 = - 7*1 + 8*0 = - 7

    Calculating vector magnitude:

    |v1| = √ (-7²+8²) = √113

    |v2| = √ (1²+0²) = 1

    cosθ = (v1 x v2) / |v1||v2| = - 7 / (√113 * 1) = - 0.659
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