[b]Definition : [/b]The absolute value of a vector is the length of the line segment representing the vector geometrically. The magnitude of the vector represented by the line segment AB i.e. [math]AB^{\rightarrow}[/math] is the length of the line segment AB. It is written as[math]\slash AB^{\longrightarrow}\slash\begin{matrix}\begin{matrix}\begin{matrix}\end{matrix}\end{matrix}\end{matrix}[/math] . If [math]a^{\longrightarrow}^{ }[/math] = (x,y) be any vector then its absolute value is given by [br][math]\slash a^{\longrightarrow}\slash=\sqrt{x^2+y^2}.[/math] Similarly, the absolute value of a space vector [math]a^{\longrightarrow}=\left(x,y,z\right)[/math] is given by [br][math]\slash a^{\longrightarrow}\slash=\sqrt{\left(x^2+y^2+z^2\right)}[/math]. If the coordinates of any point P are (x,y,z) then the absolute value of the position vector of P i.e. [math]OP^{\rightarrow}[/math] is OP = [math]\slash\left(x,y,z\right)\slash=\sqrt{\left(x^2+y^2+z^2\right)}[/math]