Calculating the resultant vector is a fundamental concept in physics and engineering. It is used to determine the net effect of two or more vectors acting on a body. The resultant vector is the vector sum of two or more vectors. It is obtained by computing the vectors based on the directions with respect to each other. The resultant vector formula has numerous applications in physics, engineering, and other fields.
There are different methods to calculate the resultant vector. One of the most common methods is the head-to-tail method. This method involves lining up the head of one vector with the tail of the other vector. The resultant vector is then drawn from the tail of the first vector to the head of the second vector. The magnitude and direction of the resultant vector can be calculated using trigonometry.
Another method to calculate the resultant vector is the parallelogram method. This method involves constructing a parallelogram using the two vectors. The diagonal of the parallelogram represents the resultant vector. The magnitude and direction of the resultant vector can be calculated using the law of cosines and the law of sines.
The resultant vector formula is of three kinds based on the direction of the vectors. These formulas are for vectors in the same direction, for vectors in the opposite direction, and for vectors inclined to each other.
Formula 1: Vectors in the same direction can be simply added to obtain the resultant vector. Here A, B are the vectors in the same direction and R is the resultant vector.
$$R = A + B$$
Formula 2: Vectors in the opposite direction are subtracted from each other to obtain the resultant vector. Here the vector B is opposite in direction to the vector A, and R is the resultant vector.
$$R = A – B$$
Formula 3: Vectors inclined to each other are computed with the below formula to obtain the resultant vector. Here the vectors A and B are inclined at an angle Ø to each other, and R is the resultant vector.
$$R^2 = A^2 + B^2 + 2ABcostheta$$
The above formulas are used to obtain the resultant value of two or more vectors. The direction of the resultant vector is determined by the angle between the vectors. The magnitude of the resultant vector is the length of the diagonal of the parallelogram formed by the vectors.
In conclusion, calculating the resultant vector is an important concept in physics and engineering. It is used to determine the net effect of two or more vectors acting on a body. The resultant vector formula has numerous applications in physics, engineering, and other fields. There are different methods to calculate the resultant vector, including the head-to-tail method and the parallelogram method. The direction and magnitude of the resultant vector can be calculated using trigonometry, the law of cosines, and the law of sines.