Vectors in Space · Superchallenge problem

How many of the following hold for ALL vectors $\mathbf u, \mathbf v, \mathbf w$ in $\mathbb R^3$? (A) $\mathbf u \times (\mathbf v \times \mathbf w) = (\mathbf u \times \mathbf v) \times \mathbf w$ (B) $(\mathbf u \times \mathbf v) \cdot \mathbf w = \mathbf u \cdot (\mathbf v \times \mathbf w)$ (C) $\lVert \mathbf u \times \mathbf v \rVert^2 + (\mathbf u \cdot \mathbf v)^2 = \lVert \mathbf u \rVert^2 \lVert \mathbf v \rVert^2$ (D) $\mathbf u \times (\mathbf v \times \mathbf w) + \mathbf v \times (\mathbf w \times \mathbf u) + \mathbf w \times (\mathbf u \times \mathbf v) = \mathbf 0$ (E) $(\mathbf u \times \mathbf v) \times (\mathbf u \times \mathbf w) = \big(\mathbf u \cdot (\mathbf v \times \mathbf w)\big)\,\mathbf u$