If \( \mathbf{a}, \mathbf{b}, \mathbf{c} \) are three non-zero vectors, then which of the follow...

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