Question

Vector has a magnitude of 6.0 m and points 30° north of east. Vector has a magnitude of 4.0 m and points 30° east of north. The resultant vector + is given by

Answers

  1. Answer:

    The resultant vector is \vec R = \vec A + \vec B = 7.196\,i + 6.464\,j.

    Explanation:

    First, each vector is determined in terms of absolute coordinates:

    6-meter vector with direction: 30º north of east.

    \vec A = (6\,m)\cdot (\cos30^{\circ} \,i + \sin 30^{\circ}\,j)

    \vec A = 5.196\,i + 3\,j

    4-meter vector with direction: 30º east of north.

    \vec B = (4\,m)\cdot (\cos 60^{\circ}\,i + \sin 60^{\circ}\,j)

    \vec B = 2\,i + 3.464\,j

    The resultant vector is obtaining by sum of components:

    \vec R = \vec A + \vec B = 7.196\,i + 6.464\,j

    The resultant vector is \vec R = \vec A + \vec B = 7.196\,i + 6.464\,j.

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