Vector Addition

Online vector calculator - add vectors with different magnitude and direction

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In mechanics there are two kind of quantities

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

vector addition parallelogram law

The procedure of "the parallelogram of vectors addition method" is

The Triangle Rule

vector addition triangle rule

The procedure of "the triangle of vectors addition method" is

Trigonometric Calculation

vector addition cosine rule

The resulting vector of two coplanar vector can be calculated by trigonometry using "the cosine rule" for a non-right-angled triangle.

FR = [ F12 + F22 − 2 F1 F2 cos(180o - (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 non-right-angled triangle.

α = sin-1 [ Fsin(180o - (α + β)) / FR ] (2)

where

α + β = the angle between vector 1 and 2 is known

Example - Calculating Vector Forces

A force 1 of magnitude 5 kN is acting in a direction 80o from a force 2 of magnitude 8 kN.

The resulting force can be calculated as

FR = [ (3(kN))2 + (8(kN))2 - 2 5(kN) 8(kN) cos(180o - (80o)) ]1/2

    = 9 kN

The angle between vector 1 and the resulting vector can be calculated as

α = sin-1[ 3(kN) sin(180o - (80o)) / 9(kN) ]

    = 19.1o

The angle between vector 2 and the resulting vector can be calculated as

α = sin-1[ 8(kN) sin(180o - (80o)) / 9(kN) ]

    = 60.9o

Online Vector Calculator

The generic calculator below can used to add vectors for velocity, forces etc.

 Magnitude of vector 1 - F1

Magnitude of vector 2 - F2

angle between vector 1 and 2 (degrees)

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Related Topics

  • Basics Basic Information as SI-system, Unit converters, Physical constants...
  • Mechanics Kinematics, forces, vectors, motion, momentum, energy and the dynamics of objects
  • Mathematics Mathematical rules and laws - areas, volumes, exponents, trigometric functions and more

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