139 a Write each vector in Figure E139 Fig E139 in terms of

1.39 - (a) Write each vector in Figure E1.39 Fig. E1.39 in terms of the unit vectors i and j. (b) Use unit vec- tors to express vector 3.00A - 4.00 B. (c) Find the magnitude and direction of C. Ä (3.60 m) C, where 70.0 1.40 You are given two vece. 30.0 tors A=-3.001 +6.00j and B = 7.001 + 2.00). Let counter- clockwise angles be positive. B (2.4 m)

Solution

1.39) Vector A = 3.6 cos 70 i + 3.6 sin 70 j

= 1.23 i + 3.38j

Vector B = -2.4 cos 30 i - 2.4 sin 30 j

= -2.07 i - 1.2j

C = 3A - 4B = 3(1.23i + 3.38j) - 4(-2.07i - 1.2j) = 7.83i + 14.94j

magnitude = sqrt(7.83^2 + 14.94^2) = 16.86 m

angle = tan^-1(14.94 / 7.83 ) = 62.34^o