The correct option is B A contains exactly one element
Let →p=(a1√2,a2√4,a3√8) & →q=(1√2,1√4,1√8) and angle between them is θ
Given that (3∑i=1ai2i)2=3∑i=1a2i2i.
⇒78(3∑i=1ai2i)2=783∑i=1a2i2i
⇒78(a12+a24+a38)2=78(a212+a224+a238)⇒78(→p⋅→q)2=|→p|2|→q|2⇒78|→p|2|→q|2 cos2θ=|→p|2|→q|2⇒|→p|=0 or cos2θ=87
cos2θ=87 is not possible. ⇒|→p|=0⇒→p=(0,0,0)⇒→a=(0,0,0)
Therefore, the equation has only one solution.