How to draw all the Electric field vectors associated with an em wave?

This is a single ray of an electromagnetic wave propagating in one dimension. But we know an electromagnetic wave travels in three dimensions.

So, I wish to draw the Electric field and magnetic field of an em wave emitted from a spherical source. If I draw the rays, It would be as below.

But Now, if I draw electric Field lines perpendicular to each of these lines, wouldn’t the Electric field of two nearby Rays interfere?

It seems that it would be impossible for each of these rays to have their $vec E$ perpendicular to the direction of propogation as two such $vec E$ would cancel each other. Can I know how to draw the Electric field in this case?

But thinking of it it is not surprising at all… How can we expect the Displacements of a 3 dimensional transverse wave to be within the 3 dimensions!How can we expect waves on surface of water to be like below!

I understand there is a difference between water waves and em waves that water waves travel in water itself but not em waves in air. But that should not make a difference because two of the rays travel in vacuum and they can still interact. Please clarify this doubt.