Plane EM wave in a vacuum, quick identity question…

Okay the question is, given a plane electromagnetic wave in a vacuum given by E=(Ex,Ey,Ez)exp[itex]^{(i(k_{x}x+k_{y}y+k_{z}z-wt)}[/itex] and B=(Bx,By,Bz)exp[itex]^{(i(k_{x}x+k_{y}y+k_{z}z-wt)}[/itex] ,
where k = (kx,ky,kz),
to show that kXE=wB.

So I’m mainly fine with the method. I can see the maxwell’s equaion ∇XE=-dB/dt, is the equation required.
-dB/dt=iwB.
And using ∇XE=ikXE, [1], the result follows.
My question is identifying equation [1]. How do you deduce this? Is it supposed to be obvious in any way. (I’ve done a check on the LHS and RHS so I can see its true), but should this be obvious?

Thanks in advance for your assistance .

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