In E⃗ and K⃗ represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by :
(ω - angular frequency) :

Solution

Physics sir · 3 steps

Get the direction from the order of the cross product, then check the size against B = E/c.

1. Direction. In an EM wave, E⃗, B⃗ and K⃗ are mutually perpendicular and follow the right-hand order E⃗ → B⃗ → K⃗. Take E⃗ along x and K⃗ along z. Then B⃗ must be along y, and z × x = y, so B⃗ points along K⃗ × E⃗.
2. Magnitude. In vacuum B = E/c and c = ω/K. So B = KE/ω, and KE is the size of K⃗ × E⃗ because the two vectors are perpendicular.

   B⃗ = 1/ω(K⃗ × E⃗)

3. So. The magnetic field vector is 1/ω(K⃗ × E⃗), which is option (a). The same result comes from Faraday's law, ∇ × E⃗ = -(∂ B⃗)/(∂ t), applied to a plane wave.

The idea to keep. For any EM wave, E⃗ × B⃗ points along the direction of travel, and B = E/c in vacuum. Use the first to fix the order of the vectors and the second to fix the factor in front.

Answer from the NTA final answer key. Solution by PrepWiser.