If $a$ , $b$ , $c$ are non-coplanar vectors then
Statement-1: $b \times c, c \times a, a \times b$ are non-coplanar.
Statement-2: $[b \times c c \times a a \times b] = 2 [a b c]^{2}$

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STATEMENT-1 is True, STATEMENT-2 is False

STATEMENT-1 is True, STATEMENT-2 is True;
STATEMENT-2 is a correct explanation for STATEMENT-1

STATEMENT-1 is False, STATEMENT-2 is True

STATEMENT-1 is True, STATEMENT-2 is True;
STATEMENT-2 is NOT a correct explanation for STATEMENT-1

answer is C.

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Detailed Solution

$\begin{array}{l} [b \times c c \times a a \times b] \\ = ((b \times c) \times (c \times a)) \cdot (a \times b) \\ = ((b \cdot (c \times a)) c - (c . (c \times a) b) \cdot (a \times b) \\ = [a \cdot b \cdot c] c \cdot (a \times b) (c \cdot (c \times a) = 0) \\ = [abc] [abc] = [a b c]^{2} \end{array}$