Orthogonality imposes independence. The opposite may not hold.
To prove it:
Take two vectors X and Y such that they are orthogonal.
let us assume that if possible they are linearly dependent.
i.e. there exists scalar c(not equal to 0)
this means, c Y^TY=0
implies, each element of Y vector is 0.which is absurd.
hence x and y are independent.
The opposite can be proved taking any counter example
x=(1 0 2)
y=(0 1 1)
the above two vectors are independent but not orthogonal.