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16 September, 06:44

Three vectors →a, →b, and →c each have a magnitude of 50 m and lie in an xy plane. Their directions relative to the positive direction of the x axis are 30°, 195°, and 315°, respectively. What are (a) the magnitude and (b) the angle of the vector →a+→b+→c and (c) the magnitude and (d) the angle of →a-→b+→c? What are the (e) magnitude and (f) angle of a fourth vector →d such that (→a+→b) - (→c+→d) = 0?

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  1. 16 September, 07:46
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    a) 38.27 b) 322.5°

    c) 126.99 d) 1.17°

    e) 62.27 e) 139.6°

    Explanation:

    First of all we have to convert the coordinates into rectangular coordinates, so:

    a = (43.3, 25)

    b = (-48.3, - 12.94)

    c = (35.36, - 35.36)

    Now we can do the math easier (x coordinate with x coordinate, and y coordinate with y coordinate):

    1.) a+b+c = (30.36, - 23.3) = 38.27 < 322.5°

    2.) a-b+c = (126.96, 2.6) = 126.99 < 1.17°

    3.) (a+b) - (c+d) = 0 Solving for d:

    d = (a+b) - c = (-40.36, 47.42) = 62.27 < 139.6°
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