Orthogonality imposes independence. The opposite may not hold.

To prove it:

Take two vectors X and Y such that they are orthogonal.

i.e. x^Ty=0

let us assume that if possible they are linearly dependent.

i.e. there exists scalar c(not equal to 0)

such that,

x=c.y

so,

x^T=cY^T

this means, c Y^TY=0

implies, 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

say,

x=(1 0 2)

y=(0 1 1)

the above two vectors are independent but not orthogonal.