# Determine resultant of two vectors using components of vector

1. F1 = 6 N, F2 = 10 N. Determine resultant vector.

Solution

F1x = F1 cos 60o = (6)(0.5) = 3 N (positive because it has same direction with x axis)

F2x = F2 cos 30o = (10)(0.53) = 53 = (5)(1.372) = -8.66 N (negative because it has same direction with -x axis)

F1y = F1 sin 60o = (6)(0.53) = 33 = (3)(1.372) = 4.116 N (positive because it has same direction with y axis)

F2y = F2 sin 30o = (10)(0.5) = -5 N (negative because it has same direction with -y axis)

Fx = F1x – F2x = 3 – 8.66 = -5.66 N

Fy = F1y – F2y = 4.116 – 5 = -0.884 N

Resultant of these two forces is 5.7 N.

2. F1 = 4 N, F2 = 4 N, F3 = 8 N. Determine resultant vector.

Solution

F1x = F1 cos 60o = (4)(0.5) = 2 N (positive because it has same direction with x axis)

F2x = -4 N (negative because it has same direction with -x axis)

F3x = F3 cos 60o = (8)(0.5) = 4 N (positive because it has same direction with x axis)

F1y = F1 sin 60o = (4)(0.53) = 23 N (positive because it has same direction with y axis)

F2y = 0

F3y = F3 sin 60o = (8)(0.53) = -43 N (negative because it has same direction with -y axis)

Fx = F1x – F2x + F3x = 2 – 4 + 4 = 2 N

Fy = F1y + F2y – F3y = 23 + 0 – 43 = -23 N

Resultant of these three forces is 5.7 N.

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