Setting $z = 0$ , $E_1 = E_2 = E$ , and taking the real part of the given equation for the electric field vector, we find that

$\begin{align*}\mathbf{E}\left(x,y,z = 0,t\right) = E\hat{\mathbf{x}}\cos \left(\omega t \right) + E\hat{\mathbf{y}}\cos \left...$
This describes a line that goes through the points $(E,-E)$ and $(-E,E)$ . Therefore, either answer a) or answer b) is correct. If the angles in answers a) and b) are the standard azimuthal angles, i.e. angles measured counterclockwise from the x-axis, then answer (B) is correct (but this is really not clear from the problem statement).

Solution to 1996 Problem 54