Get the tangent from a normal direction cg unity3d - unity3d

Question

I am writing a shader in cg where I displace the vertexes. Because I displace the vertexes, I recalculate the normals so they point away from the surface and give that information to the fragment function. In the shader I also implemented a normal map, now am I wondering shouldn't I also recalculate the tangents? And is there a formula to calculate the tangent? I read that it is on a 90 degrees angle of the normal, could I use the cross product for that?
I want to pass on the right tangent to VOUT.tangentWorld. This is my vertex function:
VertexOutput vert (VertexInput i)
{
VertexOutput VOUT;
// put the vert in world space
float4 newVert = mul(_Object2World,i.vertex);
// create fake vertexes
float4 v1 = newVert + float4(0.05,0.0,0.0,0.0) ; // X
float4 v2 = newVert + float4(0.0,0.0,0.05,0.0) ; // Z
// assign the displacement map to uv coords
float4 disp = tex2Dlod(_Displacement, float4(newVert.x + (_Time.x * _Speed), newVert.z + (_Time.x * _Speed),0.0,0.0));
float4 disp2 = tex2Dlod(_Displacement, float4(v1.x + (_Time.x * _Speed), newVert.z + (_Time.x * _Speed),0.0,0.0));
float4 disp3 = tex2Dlod(_Displacement, float4(newVert.x + (_Time.x * _Speed), v2.z + (_Time.x * _Speed),0.0,0.0));
// offset the main vert
newVert.y += _Scale * disp.y;
// offset fake vertexes
v1 += _Scale * disp2.y;
v2 += _Scale * disp3.y;
// calculate the new normal direction
float3 newNor = cross(v2 - newVert, v1 - newVert);
// return world position of the vert for frag calculations
VOUT.posWorld = newVert;
// set the vert back in object space
float4 vertObjectSpace = mul(newVert,_World2Object);
// apply unity mvp matrix to the vert
VOUT.pos = mul(UNITY_MATRIX_MVP,vertObjectSpace);
//return the tex coords for frag calculations
VOUT.tex = i.texcoord;
// return normal, tangents, and binormal information for frag calculations
VOUT.normalWorld = normalize( mul(float4(newNor,0.0),_World2Object).xyz);
VOUT.tangentWorld = normalize( mul(_Object2World,i.tangent).xyz);
VOUT.binormalWorld = normalize( cross(VOUT.normalWorld, VOUT.tangentWorld) * i.tangent.w);
return VOUT;
}
Isn't it just the vector v2 - newVert or v1 - newVert because the point along the surface? And how do I know which one of the two it is?

Answer 1

I've used something like the below:
Vector3 tangent = Vector3.Cross( normal, Vector3.forward );
if( tangent.magnitude == 0 ) {
tangent = Vector3.Cross( normal, Vector3.up );
}
Source: http://answers.unity3d.com/questions/133680/how-do-you-find-the-tangent-from-a-given-normal.html