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Let a,b,c be three non-zero vectors.Then [(a)(b)(c)]=[a]][b]][c] if and only if (1)ab=bc=0 (2)ab=ca=0 (3)bc=ca=0 (4)ab=bc=ac=0
hii[(a)(b)(c)] = a.(bxc) mod(a) mod(b) mod(c)sin(thetha)cos(alpha)This value is given equal tomod(a) mod(b) mod(c)Hence sin(thetha)cos(alpha) = 1thetha = pi/2alpha = zerohence b.c = 0 ; and a is parallel to the cross product hence perpendicular to b and c .So option D is the correct answer
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