Yes, if the angle between the two vectors is more than 90^o but less than 270⁰. (cosΘ is negative)

Log_2aa=x    then, a=(2a)^x  ......(1)

Log_3a2a=y    then,2a=(3a)^y ......(2)

Log_4a 3a=z  then, 3a=(4a)^z ......(3)

So, 

a=(2a)^x  [from (1)]

Or, a=(3a)^xy    [from(2)]

Or, a=(4a)^xyz     [from(3)]

Multiplying both sides by 4a,

4a.a=4a.(4a)^xyz  

Or,(2a)² =(4a)^{xyz + 1} 

Or,(3a)^2y =(4a)^xyz+1 

Or,(4a)^2yz =(4a)^xyz+1 

Or, 2yz = xyz+1 .proved.

Well, the propagation of light is fundamentally due to oscillation of electric field and magnetic field perpendicularly, which allows the light waves to propagate in the direction perpendicular to both the existing fields, i.e. light waves propagation solely depends on these fields.

But, sound waves are non other than the transference of energy due to disturbance, as well the propagation of sound wave has already been found to be adiabatic in nature, and through the adiabatic equation,...

At the bottom-is the correct one.

At dawn and dusk, large amount of blue and violet light(shorter wavelength) has been scattered so, the light that is recieved by an observer is mostly of a longer wavelength and therefore appears to be red.