Not even a single member ofAksionov'sfamily was concerned about his well-being when he was at his lowest.Along with the judges of the court even his wife did not trust him.Hewas imprisoned for the crime he did not commit.With time he learnt to forgive people, but he did not forget their mistreatment.

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.

Yes, a physical quantity can have magnitude and direction but still be a scalar if it doesn't obey the vector addition. An example is Electric Current which has magnitude and a fixed direction, but it does not follow vector laws of addition.