Richtingscosinussen van een vector

Consider a vector A expressed in the cartesian vector form using i, j, and k unit vectors. The magnitude of vector A is defined as the square root of the sum of squares of its components.

The direction of this vector is defined by coordinate direction angles, α, β, and γ, measured from the positive x, y, and z axes.        

These angles can be determined by the projection of A onto respective axes. These are known as the direction cosines of A.

These direction cosines can be obtained easily using unit vectors. Consider a unit vector along vector A. This unit vector can be expressed in cartesian form by dividing vector A by its magnitude.

The expressions indicate that the i, j, and k components of the unit vector represent the direction cosines of A.

Squaring the equation, a significant relationship among the direction cosines can be formulated.

Alternatively, if the magnitude and the coordinate direction angles of A are known, then it can be expressed in the Cartesian vector form.