Vector Addition
Online vector calculator  add vectors with different magnitude and direction  like forces, velocities and more.
In mechanics there are two kind of quantities
 scalar quantities with magnitude  time, temperature, mass etc.
 vector quantities with magnitude and direction  velocity, force etc.
When adding vector quantities both magnitude and direction are important. Common methods adding coplanar vectors (vectors acting in the same plane) are
 the parallelogram law
 the triangle rule
 trigonometric calculation
The Parallelogram Law
The procedure of "the parallelogram of vectors addition method" is
 draw vector 1 using appropriate scale and in the direction of its action
 from the tail of vector 1 draw vector 2 using the same scale in the direction of its action
 complete the parallelogram by using vector 1 and 2 as sides of the parallelogram
 the resulting vector is represented in both magnitude and direction by the diagonal of the parallelogram
The Triangle Rule
The procedure of "the triangle of vectors addition method" is
 draw vector 1 using appropriate scale and in the direction of its action
 from the nose of the vector draw vector 2 using the same scale and in the direction of its action
 the resulting vector is represented in both magnitude and direction by the vector drawn from the tail of vector 1 to the nose of vector 2
Trigonometric Calculation
The resulting vector of two coplanar vector can be calculated by trigonometry using "the cosine rule" for a nonrightangled triangle.
F_{R} = [F_{1}^{2} + F_{2}^{2} − 2 F_{1} F_{2} cos(180^{o}  (α + β))]^{1/2} (1)
where
F = the vector quantity  force, velocity etc.
α + β = angle between vector 1 and 2
The angle between the vector and the resulting vector can be calculated using "the sine rule" for a nonrightangled triangle.
α = sin^{1}[F_{1 }sin(180^{o}  (α + β)) / F_{R}] (2)
where
α + β = the angle between vector 1 and 2 is known
Example  Adding Forces
A force 1 with magnitude 3 kN is acting in direction 80^{o }from a force 2 with magnitude 8 kN.
The resulting force can be calculated as
F_{R} = [(3 kN)^{2} + (8 kN)^{2}  2 (5 kN) (8 kN) cos(180^{o}  (80^{o}))]^{1/2}
= 9 (kN)
The angle between vector 1 and the resulting vector can be calculated as
α = sin^{1}[ (3 kN) sin(180^{o}  (80^{o})) / (9 kN)_{ }]
= 19.1^{o}
The angle between vector 2 and the resulting vector can be calculated as
α = sin^{1}[ (8 kN) sin(180^{o}  (80^{o})) / (9 kN)_{ }]
= 60.9^{o}
Example  Airplane in Wind
A headwind of 100 km/h is acting 30^{o} starboard on an airplane with velocity 900 km/h.
The resulting velocity for the airplane related to the ground can be calculated as
v_{R} = [(900 km/h)^{2} + (100 km/h)^{2}  2 (900 km/h) (100 km/h) cos(180^{o}  (30^{o}))]^{1/2}
= 815 (km/h)
The angle between the airplane course and actual relative ground course can be calculated as
α = sin^{1}[ (100 km/h) sin((180^{o})  (30^{o})) / (815 km/h)_{ }]
= 3.5^{o}
Vector Calculator
The generic calculator below is based on equation (1) and can be used to add vectors quantities like velocities, forces etc.
Parallelogram
Resultant vectors can be estimated by drawing parallelograms as indicated below.
 draw the vectors with right direction and magnitude
 draw parallel lines to the vectors
 draw the resultant vector to the crossing point between the parallel lines
 measure the magnitude and direction of the resultant vector in the drawing
The method can also be used with more than two vectors as indicated below.
 draw the resultant vectors between two and two vectors
 draw the resultant vectors between two and two of resultant vectors
 continue until there is only one final resultant vector
 measure direction and magnitude of the final resultant vector in the drawing
In the example above  first find the resultant F_{(1,2)} by adding F_{1} and F_{2}, and the resultant F_{(3,4)} by adding F_{3} and F_{4}. The find the resultant F_{(1,2.3,4)} by adding F_{(1,2)} and F_{(3,4)}.
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