Write the direction ratio's of the vector `vec a=4hati-2hatj+hatk` and hence calculate its direction cosines.

Explanation

We know that direction ratios of a vector `vec r=xhati+yhatj+zhatk` are the respective component x,y and z of the vector. So for the given vector direction ratios is (4,-2,1).
x=4, y=-2, z=1.
The direction consines (l,m and n) of the vector is given by
`I=(4)/(sqrt(21)),m=(-2)/(sqrt(21))n=(1)/(sqrt(21))`
Thus, the direction consines are `((4)/(sqrt(21)),(-2)/(sqrt(21)),(1)/(sqrt(21)))`.