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12 May, 06:20

Vector C is 6.28 m long in a 105 degree direction. Vector D is 3.09 m long in a 233 degree direction. What is the magnitude and direction of their vector sum?

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  1. 12 May, 09:46
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    You can express the vectors in terms of their x - and y-components and add these components to receive the resulting vector.

    vector C has components:

    x = 6.28m * cos 105° = - 1.63m

    y = 6.28m * sin 105° = 6.07m

    vector D has components:

    x = 3.09 * cos 233° = - 1.86m

    y = 3.09 * sin 233° = - 2.47m

    Adding both components to get the vector sum:

    x = - 3.49m

    y = 3.6m

    You get the magnitude of the vector by using Pythagorean theorem:

    magnitude = 5.01m

    The angle ∅ is given by:

    cos∅ = x/magnitude

    Solving for ∅:

    ∅ = 134°
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