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...

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.

According to the Heisenberg Uncertainty Principle, it is impossible to determine the exact spin of an electron at any given moment. The Uncertainty Principle states that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. Spin is a form of intrinsic angular momentum, which means it does not correspond to any specific position in space, and therefore cannot be measured precisely at the same time as its position.

However, while we...

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