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How to Find Magnitude for a Given X-Component and Y-Component

The world around you is in constant motion. Displacement, velocity and acceleration are examples of vectors which provide information about the magnitude of the motion and the direction in which it occurs. All vectors describing the world around you can be resolved into components. These components are projections of the vector onto the axes of the vector's frame of reference. For two-dimensional space, each vector has an x- and a y-component. If you have the components of a vector, you can recombine these projections to discover the magnitude and directional information locked in the vector.

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Instructions

- 1
  Find the square of the X-component of the vector. For example, if the given X-component is 3 N, then the square of the X-component is 9 N^2 = (3 N)^2 = (X-component)^2.
- 2
  Find the square of the Y-component of the vector. For example, if the given Y-component is 4 N, then the square of the Y-component is 16 N^2 = (4 N)^2 = (Y-component)^2.
- 3
  Add the square of the X-component to the square of the Y-component. For example, if the given X-component is 3 N and the Y-component is 4 N, then the sum of the component squares is 25 N^2 = 9 N^2 + 16 N^2 = (3 N)^2 + (4 N)^2 = (X-component)^ 2 + (Y-component)^2.
- 4
  Find the magnitude of the vector by determining the square root of the sum of the squares of the components. For example, if the given X-component is 3 N and the Y-component is 4 N, then the square root of the sum of the component squares is 5 N = (25 N^2)^0.5 = (9 N^2 + 16 N^2)^0.5 = ((3 N)^2 + (4 N)^2)^0.5 = ((X-component)^ 2 + (Y-component)^2)^0.5.

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