Understanding Vector Addition: Calculating the Resultant Vector in Physics

The single vector which has the same effect as the original vectors acting together.

In physics, when multiple vectors act simultaneously on a point, their combined effect can be represented by a single vector known as the resultant vector

In physics, when multiple vectors act simultaneously on a point, their combined effect can be represented by a single vector known as the resultant vector. The resultant vector is calculated by adding the individual vectors together using vector addition.

Vector addition involves both magnitude and direction. To add two or more vectors, they must be expressed in terms of their components along a set of axes. The components of each vector along the axes are added separately to determine the resultant vector’s components.

To find the resultant vector, follow these steps:

1. Express each vector in terms of its components: If vector A has components (Ax, Ay) and vector B has components (Bx, By), then express the vectors as A = Ax i + Ay j and B = Bx i + By j, where i and j are unit vectors along the x and y axes, respectively.

2. Add the components of the vectors separately: Add the x-components of the vectors to obtain the x-component of the resultant vector, and similarly add the y-components to obtain the y-component of the resultant vector.

3. Express the resultant vector: Once the x-component (Rx) and y-component (Ry) of the resultant vector are obtained, express the resultant vector as R = Rx i + Ry j.

The magnitude of the resultant vector can be calculated using the Pythagorean theorem: |R| = sqrt(Rx^2 + Ry^2), where |R| represents the magnitude of the resultant vector.

The direction of the resultant vector can be found using the inverse tangent function: θ = arctan(Ry/Rx), where θ represents the angle between the resultant vector and the positive x-axis.

So, to summarize, the single vector that has the same effect as the original vectors acting together is called the resultant vector. It is found by adding the individual vectors’ components and expressing the resultant vector in terms of magnitude and direction.

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