# Determine resultant of two vectors using components of vector

Solved problems in vectors – determine resultant of two vectors using components of the vector

1. F_{1} = 6 N, F_{2} = 10 N. Determine resultant vector.

Solution

F_{1x} = F_{1} cos 60^{o} = (6)(0.5) = 3 N (positive because it has same direction with x axis)

F_{2x }= F_{2} cos 30^{o} = (10)(0.5√3) = 5√3 = (5)(1.372) = -8.66 N (negative because it has same direction with -x axis)

F_{1y} = F_{1} sin 60^{o} = (6)(0.5√3) = 3√3 = (3)(1.372) = 4.116 N (positive because it has same direction with y axis)

F_{2y} = F_{2} sin 30^{o} = (10)(0.5) = -5 N (negative because it has same direction with -y axis)

F_{x} = F_{1x }– F_{2x }= 3 – 8.66 = -5.66 N

F_{y} = F_{1y }– F_{2y }= 4.116 – 5 = -0.884 N

Resultant of these two forces is 5.7 N.

2. F_{1} = 4 N, F_{2} = 4 N, F_{3} = 8 N. Determine resultant vector.

Solution

F_{1x} = F_{1} cos 60^{o} = (4)(0.5) = 2 N (positive because it has same direction with x axis)

F_{2x }= -4 N (negative because it has same direction with -x axis)

F_{3x }= F_{3} cos 60^{o} = (8)(0.5) = 4 N (positive because it has same direction with x axis)

F_{1y} = F_{1} sin 60^{o} = (4)(0.5√3) = 2√3 N (positive because it has same direction with y axis)

F_{2y} = 0

F_{3y} = F_{3} sin 60^{o} = (8)(0.5√3) = -4√3 N (negative because it has same direction with -y axis)

F_{x} = F_{1x }– F_{2x }+ F_{3x} = 2 – 4 + 4 = 2 N

F_{y} = F_{1y }+ F_{2y }– F_{3y} = 2√3 + 0 – 4√3 = -2√3 N

Resultant of these three forces is 5.7 N.

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