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A, B and $\mathbf{C}$ are three non-collinear, non co-planar vectors. What can you say about direction of $\mathbf{A} \times(\mathbf{B} \times \mathbf{C}) ?$
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The direction of $(\mathbf{B} \times \mathbf{C})$ will be perpendicular to the plane containing by vector $\mathbf{B}$ and $\mathbf{C}$ by right hand thumb rule. $\mathbf{A} \times(\mathbf{B} \times \mathbf{C})$ will lie in the plane containing $\mathbf{B}$ and $\mathbf{C}$ and is perpendicular to vector $\mathbf{A}$.
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