Consider a vector A, the unit vector A is a vector having a magnitude of unity and same direction as given vector i.e. A. We can write
For a Cartesian co-ordinate system shown in Fig \(\hat{i},\hat{j}\) and \(\hat{k}\) are unit vector along x, y and z–axis. P is a point having co-ordinates (x, y, z). OP = r = position vector of P in terms of \(\hat{i},\hat{j}\) and \(\hat{k}\)
\(r = x\hat{i}+y{j}+z\hat{k}\)
|r| = r = Magnitude of position vector = \(\sqrt{x^2+y^2+z^2}\)
Let α ,β and γ be angle OP makes with x, y and z–axis respectively. Then
cos α, cos β and cos γ are known as direction cosines of r.
