^{(1) Hint: The resultant of three vectors will be equal to zero only if the vectors are coplanar.}

^{Step 1: Find if the vectors are coplanar.}

^{Given, A + B + C = 0}

^{Hence, we can say that A, B, and C are in one plane and are represented by the three sides of a triangle taken in one order.
Step 2: Find the incorrect statements one by one.}

^{$\begin{array}{l} \mathrm{B}\times (\mathrm{A}+\mathrm{B}+\mathrm{C})=\mathrm{B}\times 0=0\\ \Rightarrow \mathrm{B}\times \mathrm{A}+\mathrm{B}\times \mathrm{B}+\mathrm{B}\times \mathrm{C}=0\\ \Rightarrow \mathrm{B}\times \mathrm{A}+0+\mathrm{B}\times \mathrm{C}=0\\ \Rightarrow \mathrm{B}\times \mathrm{A}=-\mathrm{B}\times \mathrm{C}\\ \Rightarrow \mathrm{A}\times \mathrm{B}=\mathrm{B}\times \mathrm{C}\\ \therefore (\mathrm{A}\times \mathrm{B})\times \mathrm{C}=(\mathrm{B}\times \mathrm{C})\times \mathrm{C}\end{array}$}

^{It cannot be zero as $\begin{array}{l}\end{array}$$\begin{array}{l}(\mathrm{B}\times \mathrm{C})\times \mathrm{C}\end{array}$$\begin{array}{l}\mathrm{can\; not\; be\; zero\; unless\; B\; and\; C\; are\; parallel\; to\; each\; other.\; Hence\; statement (a)\; is\; correct.}\end{array}$}

If B and C are not parallel, then (AxB) will be perpendicular to the plane of A, B and C.
Hence, (AxB).C = 0 whatever be the situation is. Hence, statement (b) is incorrect and option.
Also, (AxB)xC will be in the plane of A, B and C and statement (c) is correct.
Statement (d) is also incorrect as discussed already.