Addition of two vectors may be affected with the help of parallelogram law of addition.
The resultant(sum) vector R’ of A’ and B’ is the diagonal of the parallelogram of A and B of adjacent sides.
The triangular law of vector addition follows the parallelogram law which states that: if the tail-end of the vector is placed at the arrow-head of the vector, their resultant(sum) vector is drawn from the tail of the first to the head of the other.
see the figure below
Subtraction of vectors
The figure below shows addition of vectors in reverse direction of B’ vector.
The process of subtracting one algebraic quantity from one another is equivalent to adding the negative of the quantity to be subtracted. in essence, a-b = a+(-b)
The negative vector –B‘ of vector B is defined as a vector of the same magnitude(length) but in opposite direction.
Resultant set of forces
Two vectors are said to be equal if they have the same magnitude and direction. If two vectors A and B are parallel, the magnitude of vector sum C equals the sum of magnitudes of A and B.
consider the vectors A and B represented below
The resultant vector C will be represented by a single vector as shown
If two vectors are antiparallel, the magnitude of a vector equals the difference of the magnitudes of A and B
The diagram below shows vectors that represents forces acting in opposite direction
The resultant vector is smaller than the larger vector and bigger than the smaller vector and moves in the direction of the larger vector.
Related Topics
References
- Sanny, J. S., & Ling, S. (2016). University Physics Volume 1. OpenStax. https://doi.org/13: 9781938168161
- Abbott, A. F. (1989). PHYSICS (5th ed.). Heinemann. https://doi.org/978043567014