**Toolbox:**

- If $ l, m , n$ are the d.c.s of a vector, then $ l^2+m^2+n^2=1$

$ Cos^2 30^{\circ} +Cos^2 45^{\circ} +Cos^2 60^{\circ} = \large\frac{3}{4}+ \large\frac{1}{2}+ \large\frac{1}{4}= \large\frac{3}{2} \neq 1$

A vector cannot have direction angles $ 30^{\circ}, 45^{\circ}, 60^{\circ}$