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 to
mod(a) mod(b) mod(c)

Hence sin(thetha)cos(alpha) = 1

thetha = pi/2

alpha = zero

hence b.c = 0 ; and a is parallel to the cross product hence perpendicular to b and c .

So option D is the correct answer