Write down a unit vector in XY- plane, making an angle of 30∘ in anticlockwise direction with the positive direction of X-axis.
Let OP make 30∘ with X-aixs, 60∘ with Y-axis and 90∘ with Z-axis and it lies in XY-plane.
∴ Direction cosines of OP are cos 30∘, cos 60∘ and co 90∘ i.e.,√2,12,0. Thus,OP is √2 ^i+12 ^j,
which is required unit vector in XY-plane.