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a, b and each have a magnitude of 50.0 m and lie in an xy plane. Their directions relative to Three vectors the positive direction of the x axis are 31.0194°, and 313 , respectively. What are (a) the magnitude and (b) the angle of the vector a b C (relative to the +x direction in the range of (-180°, 180°)), and (c) the magnitude and (d) the angle of a b + C - in the range of (-180°, 180°)? what are (e) the magnitude and (f) the angle (in the range of (-180°, 180°)) of a fourth vector d such that ( a + b )-( c + d )-O ? (a) Number (b) Number (c) Number (d) Number (e) Number (f) Number Unit Unit Unit Unit Unit Unit
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part (a) and (b) We shall first sum all the components in x direction and then in y direction x-acos(31) bos(194°) + ccos(313°) 0.857 0.970 0.682 0.569 Y- asin(31°) +bsin(194°) + csin (313°) 0.515 0.242 - 0.732 0.458 So, The resultant vect0.569 +0.458ý Magnitude - V0.5692 +0.4580.533 0.458) 38.83 tan-1 (0.558)-38.8r tan 0.569 Angle wrt x axis-

part (c)and (d) Fora -6+-, we see now that -6 makes an angle of 194-180-14 with the+x axis. Again, we shall first sum all the components in x direction and then in y direction, x-aco(31)+bcos(14) +ccos(313°) Σ x =0.857 +0.970+0.682-2.509 Y-asin(31°) +bsin(14°) +csin(313°) Σ Y-0515 + 0.242-0.732-0025 So, The resultant vecto2.509 +0.025j Magnitude - V2.5092 +0.025-6.296 on-1 0.025 Angle wrt x axis = 2.509 ) = 0.570

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