How to determine the resultant vector in vector addition?

The resultant vector in vector addition is determined by adding together the magnitudes and directions of the individual vectors.

In more detail, vector addition involves combining two or more vectors to produce a single vector, known as the resultant vector. This process is based on the principles of trigonometry and geometry.

To begin with, you need to understand that vectors have both magnitude (size) and direction. When adding vectors, you must take into account both of these properties. The resultant vector's magnitude is the sum of the magnitudes of the individual vectors, and its direction is determined by the directions of the individual vectors.

There are two main methods for adding vectors: the head-to-tail method and the parallelogram method.

In the head-to-tail method, the first vector is drawn, then the second vector is drawn with its tail at the head of the first vector. The resultant vector is then drawn from the tail of the first vector to the head of the second vector.

In the parallelogram method, both vectors are drawn with their tails at the same point. A parallelogram is then completed using these two vectors as sides, and the resultant vector is drawn from the common tail point to the opposite corner of the parallelogram.

In both methods, the magnitude of the resultant vector can be calculated using the Pythagorean theorem if the vectors are at right angles, or the law of cosines if they are not. The direction of the resultant vector can be calculated using the law of sines.

Remember, the resultant vector represents the total effect of the individual vectors. So, understanding how to determine it is crucial in physics, where vectors are used to represent quantities such as force, velocity, and displacement.