Let the unit vector is a in XY-plane

So a = xi + yj .............1

where unit vector in the direction of x-axis is i and in y-axis is j

Now given that a makes an angle of 30 with x-axis

So a.i = |a|*|i|*cos 30

=> a.i = 1*1*√3/2   (since a and i are unit vector so |a| = 1, |i| = 1 )

=> a.i = √3/2

=> (xi + yj + 0k).(1i + 0j + 0k) = √3/2

=> x = √3/2                           (i.i = j.j = k.k = 1)

Again since a makes an angle of 30 with x-axis then a makes an angle of 60 with y-axis

So a.j = |a|*|j|*cos60

=>(xi + yj + 0k).(0i + 1j + 0k) = 1/2

=> y = 1/2

Now put value of x and y in equation 1, we get

a = (√3/2)i + (1/2)j

So unit vector is (√3/2)i + (1/2)j