Determine resultant of two vectors using components of vector

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

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

Solution

F_1x = F₁ cos 60^o = (6)(0.5) = 3 N (positive because it has same direction with x axis)

F_2x = F₂ 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 = F₁ 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 = F₂ 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. F₁ = 4 N, F₂ = 4 N, F₃ = 8 N. Determine resultant vector.

Solution

F_1x = F₁ 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 = F₃ cos 60^o = (8)(0.5) = 4 N (positive because it has same direction with x axis)

F_1y = F₁ sin 60^o = (4)(0.5√3) = 2√3 N (positive because it has same direction with y axis)

F_2y = 0

F_3y = F₃ 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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