VECTOR ADDITION

INPUT   DATA ♥ EXAMPLE Of Input/Output

Title  

Vector  Magnitude   Angle (anticlockwise +ve)  
#    °  
1
2
3
4
5
6
7
8
9
10  
11
12

     Reset

OUTPUT   VARIABLES   &   GRAPHS

Vector   Magnitude   Angle  X-component   Y-component  
  °
1
2
3
:
11
12
Totals
 ♦ Resultant
THEORY  &   FORMULAE

Vector Summation

A vector quantity is one that has both magnitude (size) and direction. Examples include displacement, velocity, acceleration, force and momentum. The Resultant vector is the sum of a number of vectors of a particular type, such that its effect is the same as all the original vectors taken together.

Consider a series of n coplanar vectors of magnitudes V1, V2,...,Vi, ...Vn, with corresponding directions θ1, θ2,...,θi, ...θn. These vectors can be resolved into the x- and y- components and summed as follows:

  Vx = ∑Vicosθi
  Vy = ∑Visinθi
  VR = √[Vx2 + Vy2]
  θR = tan-1[Vy/Vx]

where
     Vx = component of resultant vector in x-direction
     Vy = component of resultant vector in y-direction
     VR = magnitude of resultant vector
     θR = direction of resultant vector

Because the arctan function gives value only in the [-π/2,+π/2] range (ie. quadrant I & IV), due consideration is made to derive the correct direction for the case where the resultant direction falls in quadrant II or III.

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point

BIBLIOGRAPHY