2# Force Vector (2D)

Define Force vector?

A force vector is a representation of a force that has both magnitude and direction. This is opposed to simply giving the magnitude of the force, which is called a scalar quantity.

Free Vector

Situations in which the vectors may be positioned anywhere in the space without the loss or change, provided the magnitude and direction are kept constant.

Sliding Vector

Situations in which the vector may be moved anywhere along its line of action in the space without change of meaning.

Fixed or Bound Force Vector

Situations in which the vectors must be applied at definite points. If the point of application is changed it will give different results.

Note: All quantities that have magnitude and direction and that add according to the parallelogram law are called Vector Quantities. 

Methods of Addition/Subtraction of Force Vectors

Head to Tail method:

This involves drawing vectors to scale on a sheet of paper beginning at a designated starting position. Where the head of the first vector ends, the tail of the second vector begins. The resultant is then drawn from the tail of the first vector to the head of the second vector.


A parallelogram is a four sided figure with opposite sides parallel and equal in length.

Force Vector


Use of law of sine and cosine to determine magnitude and direction.

Vector space


F=Fx + Fy

(FR)X = ∑FX

(FR)Y = ∑FY




important notes

  • The resultant of several coplanar forces can easily be determined if an x, y coordinate system is established and the forces are resolved along the axis.
  • The direction of each force is specified by the angle of its line if action making with one of the axes or by a slope of triangle.
  • The orientation of the x and y axes is arbitrary and their positive direction can be specified by the Cartesian Unit vector i and j.
  • The x and y components of the resultant force are simply the algebraic addition of the components of the coplanar forces.
  • The magnitude of the resultant force is determined from the Pythagorean Theorem.

you may revisit the introduction to this course