RedCrab Math Tutorial

# Calculate magnitude of a vector

This article describes how to calculate the magnitude of a vector. The magnitude of a vector is the length of the vector and can be calculated using the Pythagoras theorem. According to this, the square of the hypotenuse is equal to the sum of the squares of the catheters. The lengths of the catheters correspond to the respective coordinates of the vector.
The following illustration shows a vector in a plane. The length of the vector corresponds to the length of the hypotenuse of a right triangle.

We can therefore calculate:

The same procedure applies to vectors with more than two elements.

Examples:

Practice Example:

A ball is shot horizontally with a force of four Newtons. It also has a downward vertical force of 3 Newton. The resulting force runs in the direction of the diagonal of the rectangle formed by the two output vectors.

The calculation is

 Vector Definition Vector Calculation Vector Addition Vector Subtraction Vector Magnitude Vector Scalar Product Angle between two Vectors

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