Here, \(\vec E\) = 5 x 103\(\hat i\) N/C, i.e., field is along positive direction of X - axis.
Surface area, A = 10 cm x 10 cm = 0.10 m x 0.10 m = 10-2m2
(i) When plane is parallel to Y-Z plane, the normal to plane is along X - axis. Here
θ = 0°
(ii) When the plane makes a 30° angle with the X-axis, the normal to its plane makes 60° angle with X - axis.
Hence θ = 60°