How to find the vector module

How to find the vector module

In mathematics and physics "module" it is accepted to call the absolute value of any size which is not considering its sign. In relation to a vector it means that its direction should be ignored, considering a usual piece of a straight line. In this case the problem of finding of the module comes down to calculation of length of such piece set by coordinates of an initial vector.


1. Use Pythagorean theorem for calculation of length (module) of a vector - it is the simplest and clear method of calculation. That to make it consider the triangle made of the vector and its projections to axes of a rectangular two-dimensional (Cartesian) system of coordinates. It is a rectangular triangle in which legs will be projections, and a hypotenuse - a vector. According to Pythagorean theorem for finding of length of a hypotenuse necessary to you to put squares of lengths of projections follows and to take a square root from result.

2. Calculate lengths of projections for use in a formula from the previous step. For this purpose follows it is equal X -X ₂, and on ordinate axis - Y -Y ₂. At the same time does not matter which coordinate of a point to consider deductible, and by which - reduced as in a formula their squares will be used that will automatically reject signs of these sizes.

3. Substitute the received values in the expression formulated in the first step. The required module of a vector will be equal to a square root from the sum of the squared differences of coordinates of initial and final points of a vector along the corresponding axes in two-dimensional rectangular coordinates: √ ((X -X ₂)²+ (Y -Y ₂)²).

4. If the vector is set in the three-dimensional system of coordinates, then use a similar formula, having added to it third composed which is formed by coordinates along an axis of z-coordinates. For example, if to designate the initial point of a vector by coordinates (X ₁, Y ₁, Z ₁), and final - (X ₂, Y ₂, Z ₂), then the formula of calculation of the module of a vector will take such form: √ ((X -X ₂)²+ (Y -Y ₂)²+ (Z -Z ₂)²).

Author: «MirrorInfo» Dream Team