How is the resultant of two vectors determined?

The resultant of two vectors is determined by either the graphical method, parallelogram method, or the analytical method.

The graphical method involves drawing the vectors to scale on a graph paper, placing them head to tail, and then drawing the resultant from the tail of the first vector to the head of the last vector. This method is simple and intuitive, but it's not very accurate because it relies on your ability to draw and measure accurately.

The parallelogram method is a bit more complex. It involves drawing the vectors as two adjacent sides of a parallelogram, and then drawing the diagonal of the parallelogram from the common point of the vectors. This diagonal represents the resultant vector. This method is more accurate than the graphical method, but it's also more difficult to perform, especially for complex vectors.

The analytical method is the most accurate and the most complex. It involves breaking down the vectors into their components, adding or subtracting these components as necessary, and then recombining them to find the resultant vector. This method requires a good understanding of trigonometry and vector operations, but it's the best method for finding the resultant of two or more vectors.

In all these methods, it's important to remember that vectors have both magnitude and direction. The magnitude of the resultant vector is found by using the Pythagorean theorem or trigonometric functions, and the direction is found by using trigonometric functions or by measuring the angle from a reference line.

In summary, the resultant of two vectors can be found by either graphical, parallelogram, or analytical methods. Each method has its advantages and disadvantages, and the choice of method depends on the complexity of the vectors and the level of accuracy required.