What is the parallelogram formula for resolving vectors
The formula for resolving vectors in a parallelogram can be derived from the fact that a parallelogram law of vector addition states that the vector sum of two vectors can be represented by the diagonal of the parallelogram formed by those vectors.
To resolve a vector into its components using the parallelogram law, you can use the following formulas:
1. To find the horizontal component (x-component) of a vector:
- Multiply the magnitude of the vector by the cosine of the angle it makes with the horizontal axis.
Horizontal Component (Rx) = |V| * cos(θ)
2. To find the vertical component (y-component) of a vector:
- Multiply the magnitude of the vector by the sine of the angle it makes with the horizontal axis.
Vertical Component (Ry) = |V| * sin(θ)
The result of these calculations gives you the respective components of the vector in the coordinate system.
Note: The angle θ is measured from the positive x-axis counterclockwise to the vector. The magnitude of the vector is denoted by |V|.