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26 May, 02:54

Obtain expressions in component form for the position vectors having the following polar coordinates: (a) 12.8 m, 150° (b) 3.30 cm, 60.0° (c) 22.0 in., 215°.

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  1. 26 May, 05:22
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    a) 12.8 m, 150° = (-11.09 i + 6.4 j) m

    b) 3.30 cm, 60.0° = (1.65 i + 2.86 j) cm

    c) 22.0 in., 215° = (-18.02 i + 9.30 j) in.

    Explanation:

    Consider vector having magnitude X and inclined θ degree to positive horizontal axis, its horizontal component = X cosθ and vertical component = X sinθ.

    So X = X cosθ i + X sinθ j

    a) 12.8 m, 150°

    = 12.8 cos 150 i + 12.8 sin 150 j = (-11.09 i + 6.4 j) m

    b) 3.30 cm, 60.0°

    = 3.30 cos 60 i + 3.30 sin 60 j = (1.65 i + 2.86 j) cm

    c) 22.0 in., 215°

    = 22.0 cos 215 i + 22.0 sin 215 j = (-18.02 i + 9.30 j) in.
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