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°.

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.