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.

1. Statement; true
2. Statement; false
3. Statement; true
4. Interrogative sentence; not a statement
5. Imperative sentence; not a statement
6. Exclamatory sentence; not a statement

The two vectors (say A and B) of different magnitudes cannot be combined to give zero resultant since minimum value of combination is ІA-BІ which is not zero if AB.

The three vectors A, B and C of different magnitudes can be zero such that they form a closed triangle, then,

      A+B+C=0

or, C=-(A+B)

Hence, the sum of three vectors may be zero if vector sum of any two vectors is equal and opposite to the third vector.

Note: The vectors can give this result only if...