Thread: 3 orthogonal vectors

in 3D space, if the projection of vector "U" onto vector "V"= vector "W1" then
U=W1+W2 so W2=U-W1 and the dot product of W2 and W1=0
can anyone please help me find the third vector "W3" so that the dot product of "W3" and "W2"=0 and the dot product of "W3" and "W1"=0. In other words, all three are mutually orthogonal and all three should add up to vector "U"

, the cross product, is perpendicular to both.