Hi Abhyudaya.. :)
Only Statement 3 is correct.
To rule out statement 1, use the following example:
n=2, x=(-1,-2) , y=(2,3)
To rule out statement 2, use the following example:
n=2 , x=(-1,-2)
Statement 3 proof:
LHS: x*cy = ∑xi|cyi| = c∑xi|yi| [As c is strictly positive]
RHS: c(x*y) = c∑xi|yi|
LHS=RHS
Hence, proved.
:)