3.14.
Visualize:
G
G G
G
G
K
(a) We have A = 5iˆ + 2 ˆj, B = −3iˆ − 5 ˆj, and − B = +3iˆ + 5 ˆj. Thus, D = A + ( − B) = 8iˆ + 7 ˆj.
G G
G
(b) Vectors A, B and D are shown in the above figure.
G
G
(c) Since D = 8iˆ + 7 ˆj = Dxiˆ + Dy ˆj , Dx = 8 and Dy = 7. Therefore, the magnitude and direction of D are
Solve:
D = (8) 2 + (7) 2 = 10.6
Assess:
⎛ Dy ⎞
−1 ⎛ 7 ⎞
⎟ = tan ⎜ ⎟ = 41°
⎝8⎠
⎝ Dx ⎠
θ = tan −1 ⎜
Since | Dy | < | Dx | , the angle θ is less than 45°, as it should be.