Direction cosines of a vector

Direction Cosines of a vector
Let [math]OP^{\rightarrow}[/math] be any vector making the angles [math]\alpha[/math], [math]\beta[/math] and [math]\gamma[/math] with the positive X-,Y- and Z- axes respectively. Then the cosines of the angles [math]\alpha[/math], [math]\beta[/math] and [math]\gamma[/math] are called the direction cosines of the vector [math]OP^{\rightarrow}[/math]. They are denoted by l = cos[math]\alpha[/math], m =cos[math]\beta[/math] and n = cos[math]\gamma[/math]. If [math]OP^{\rightarrow}[/math]= (x,y,z) then cos[math]\alpha[/math] =[math]\frac{x}{\sqrt{x^2+y^2+z^2}}[/math], cos[math]\beta[/math]=[math]\frac{y}{\sqrt{x^2+y^2+z^2}}[/math] and cos[math]\gamma[/math] =[math]\frac{z}{\sqrt{x^2+y^2+z^2}}[/math] where,[math]\frac{x}{\sqrt{x^2+y^2+z^2}}[/math], [math]\frac{y}{\sqrt{x^2+y^2+z^2}}[/math] and [math]\frac{z}{\sqrt{x^2+y^2+z^2}}[/math] are the x-,y- and z- component of the unit vector in the direction of the vector [math]OP^{\rightarrow}[/math].

Information: Direction cosines of a vector