Assertion (A): For an electromagnetic wave propagating in vacuum...

The direction of propagation of an electromagnetic wave is given by the cross product of the electric and magnetic field vectors, i.e., $\vec{v} \parallel \vec{E} \times \vec{B}$.

Given that the wave propagates along the negative z-axis, the direction of propagation is $-\hat{k}$.

The electric field is along the positive x-axis, so $\vec{E}$ is along $+\hat{i}$.

We need to find the direction of $\vec{B}$ such that $\hat{i} \times \vec{B} = -\hat{k}$.

Since $\hat{i} \times \hat{j} = \hat{k}$, it follows that $\hat{i} \times (-\hat{j}) = -\hat{k}$.

Therefore, the magnetic field must be along the negative y-axis ($-\hat{j}$).

The Assertion states that the magnetic field is along the positive y-axis, which is incorrect. The Reason correctly states the principle for finding the propagation direction. Thus, Assertion (A) is false but Reason (R) is true.

Answer: Assertion (A) is false but Reason (R) is true