Define resultant of two vectors
The resultant of two vectors is a vector that represents the combination of the two individual vectors. It describes the net effect of both vectors acting together.
To determine the resultant of two vectors, you need to consider both the magnitudes and directions of the vectors:
1. Start by placing the two vectors in a coordinate system. Each vector will have its own magnitude and direction.
2. To find the resultant vector, add the corresponding components of each vector. Add the x-components together and the y-components together. This will give you a new vector with the sum of the x-components and the sum of the y-components.
3. To determine the magnitude of the resultant vector, use the Pythagorean theorem. The magnitude is found by taking the square root of the sum of the squares of the x-component and the y-component.
4. To determine the direction of the resultant vector, use trigonometry. The direction can be found by taking the inverse tangent of the quotient of the y-component to the x-component. This will give you an angle measured from the positive x-axis.
Overall, the resultant of two vectors is found by adding their components, finding the magnitude using the Pythagorean theorem, and calculating the direction using trigonometry.