A line in space makes equal positive angles with the x- and y-axes and an angle of 60∘ with the z-axis.
(i) If l,m,n are the direction cosines of the line, establish the system of equations that these numbers must satisfy.
(ii) Solve the system obtained in part (i) to find the direction cosines of the line.
(iii) Write one set of corresponding direction ratios for the line.