causality test in cointegrated VEC

[alettore]

Say you have a tri-variate VEC with endogenous x1,x2 and x3 and cointegration rank 2.
Hence the equation of x1 would be
Dx1 = a11(first cointegration vector) + a12(second cointegration vector) + lagged endogenous
similarly the other endogenous would be
Dx2 = a21(first cointegration vector) + a22(second cointegration vector) + lagged endogenous
Dx3 = a31(first cointegration vector) + a32(second cointegration vector) + lagged endogenous

If
1) the first cointegration vector is normalised with X1
2) the second cointegration vector is normalised with X2

and
the test a12=0 is rejected

then
does it mean the second cointegration vector (i.e. x2) "causes" the first endogenous?

Please help with interpretation!!!!