STD 12 - 10. vector algebra — JEE कक्षा 11 साइन्स — Question

$(b \times c) \times (c \times a) = ((b \times c)\,.\,a)c - ((b \times c)\,.\,c)a = [\,b\,c\,a]\,c$

$(c \times a) \times (a \times b) = ((c \times a)\,.\,b)a - ((c \times a)\,.\,a)b = [c\,a\,b]\,a$

$\therefore \,\,\,[(a \times b) \times (b \times c)(b \times c) \times (c \times a)(c \times a) \times (a \times b)]$

$ = [[a\,b\,c]\,a\,[a\,b\,c]\,b\,[a\,b\,c]\,c]$$ = {[a\,b\,c]^3}[a\,b\,c] = {[a\,b\,c]^4}.$