Lesson 7: Summary on Graphical Method of Addition of Vectors in Two Dimensions (2-D)
- There are two primary methods for determining the vector sum of two or more vectors: the Graphical method and the Analytic (algebraic) method.
- When adding vectors, it’s essential that they have the same units; for instance, it doesn’t make sense to add a force vector measured in newtons to a velocity vector measured in meters per second.
- The same rule applies to scalars; adding mass to volume or density to time intervals is equally meaningless.
- The graphical method of vector addition involves using equal vectors.
- A vector can be displaced parallel to itself without altering its properties, a process known as translating a vector.
- One of the graphical methods is the Triangle Law of Vector Addition. In this method, if a particle undergoes a displacement followed by another displacement, the result is the same as if the particle had undergone a single displacement. This resultant displacement is symbolized by placing vectors head to tail and drawing an arrow from the tail of the first vector to the head of the second vector.
- Another graphical method is the Parallelogram Law of Vector Addition.
- In this method, two vectors are placed tail to tail, and a parallelogram is constructed using these vectors as sides.
- The diagonal of the parallelogram, drawn from the common tail point to the opposite corner, represents the resultant vector.
- For adding more than two vectors, the Polygon Law of Vector Addition is used.
- This involves placing each subsequent vector’s tail to the head of the previous vector.
- The resultant vector is then drawn from the tail of the first vector to the head of the last vector.
- Vector subtraction is also possible, which involves adding a vector of the same magnitude but in the opposite direction.
- The difference between two vectors A and B is defined as the vector sum of A and -B.
- These methods of vector addition and subtraction are crucial for accurately analyzing and solving various physical problems.