How are vector quantities represented?
A force is a vector, it has magnitude and direction. Its SI unit is the Newton (N). At any time, two or more forces may be acting on an object. the forces may have different magnitudes and directions. In such cases, we can use vector diagrams to add up these forces.
In a vector diagram, a vector quantity is represented by an arrow. The length of the arrow is proportional to the magnitude of the vector. The direction of the arrow indicates the direction of vector.
The diagram shows the vector diagram of a force of 20 N in the direction 45 degrees north of east.
How to we add vectors?
Scalar quantities ( or scalars) such as distance and speed have only magnitude. When we add scalars, we add their magnitudes only.
Unlike scalars, vector quantities have magnitude and direction. When we add two or more vectors, we cannot add their magnitudes only. We need to find a single vector that produces the same effect as the vectors combined. The single vector, called the resultant vector, must be equivalent to the individual vectors combined in terms of magnitude and direction.
Addition of parallel vectors
Let us assign the direction towards the right as positive. Diagram shows two parallel forces of magnitude 3 N and 5 N acting on a block. Both forces act in the same direction ( towards the right). The resultant force is 8 N ( 3 + 5 = 8) and is directed towards the right. A resultant vector is usually indicated by double-headed arrow.
In the diagram, the two forces are still parallel but act in the opposite directions. The resultant force is 2 N (5 + (-3) = 2) and is directed towards the right.
In diagram, two parallel forces of 3 N act on the block in the opposite directions. This produces zero resultant force.
Addition of non-parallel vectors
There are two methods of adding non parallel vectors: the parallelogram method and the tip-to-tail method. Both methods give the same equivalent vector.
Consider two forces, 5 N and 3 N, acting on a block. The forces don't act along the same line ( they are not parallel). The diagram demonstrates how we can obtain the resultant force.
By either the parallelogram method or the tip-to-tail method, we arrive at the same answer: the resultant vector has magnitude of 7 N and acts at an angle of 18 degrees to the horizontal.
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