Solving a Moment Equation: Understanding the Relationship with AD

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because when rE x W and rb xTB are not perpendicular to u , then i can't say that u . (rE x W) and u .(rb xTB ) = 0

Nobody is saying those two dot products are individually zero.
The balance of torques gives us that rE x W + rb x TB + rDA x force_at_A = 0.
We take the dot product of that with u to obtain the equation u.(rE x W) + u.(rb x TB) + u.(rDA x force_at_A) = 0.
We then observe that since u is parallel to rDA the triple product u.(rDA x force_at_A) must be zero.
From that we conclude u.(rE x W) + u.(rb x TB) = 0.
This does not tell us anything about whether u is parallel to any of the four other vectors in that equation.