If \( a, b, c \) are three non-zero vectors, then which of the following statement(s) is/are tru...

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If \( a, b, c \) are three non-zero vectors, then which of the following statement(s) is/are true?
(a) \( \mathbf{a} \times(\mathbf{b} \times \mathbf{c}), \mathbf{b} \times(\mathbf{c} \times \mathbf{a}), \mathbf{c} \times(\mathbf{a} \times \mathbf{b}) \) form a right handed system
(b) \( c,(a \times b) \times c, a \times b \) form a right handed system
(c) \( \mathbf{a} \cdot \mathbf{b}+\mathbf{b} \cdot \mathbf{c}+\mathbf{c} \cdot \mathbf{a}0 \) if \( \mathbf{a}+\mathbf{b}+\mathbf{c}=0 \)
(d) \( \frac{(a \times b) \cdot(b \times c)}{(b \times c) \cdot(a \times c)}=-1 \) if \( a+b+c=0 \)
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