Answer
a)
A= 1.23i + 3.38j
B= -2.078i + (-1.2)j
b) 12.0i + 14.9j
c) 19.2 m, 51.2°
Work Step by Step
a)
A= 3.60 m
Ax= Acos(70) = 3.60 x cos(70) = 1.23 m= 1.23i
Ay= Asin(70) = 3.60 x sin(70) = 3.38 m= 3.38j
B= 2.4. m
Bx= Bcos(30)= 2.4 x cos(30) = -2.078 m= -2.08i
By= Bsin(30)= 2.4 x sin(30) = -1.20 m = -1.20j
b)
C= 3(A) - 4(B)
C= 3(1.23i + 3.38j) - 4((-2.08i) + (-1.2j))
C= 3.69i + 10.14j + 8.32i + 4.8j
C= 12.01i + 14.94j = 12.0i + 14.9j
c)
C= ((12.01)^2 + (14.94)^2)^1/2= 19.16 m = 19.2 m
\theta= Tan^-1(14.94/12.01) = 51.2°
