If $\overline{\mathrm{a}}=2 \overline{\mathrm{i}}-3 \overline{\mathrm{j}}+4 \overline{\mathrm{k}}, \overline{\mathrm{b}}=\overline{\mathrm{i}}+2 \overline{\mathrm{j}}-\overline{\mathrm{k}}, \overline{\mathrm{c}}=3 \overline{\mathrm{i}}-\overline{\mathrm{j}}+2 \overline{\mathrm{k}}$ and $\overline{\mathrm{d}}=\overline{\mathrm{i}}+\overline{\mathrm{j}}+\overline{\mathrm{k}}$ are four vectors, then $(\overline{\mathrm{a}} \times \overline{\mathrm{b}}) \times(\overline{\mathrm{c}} \times \overline{\mathrm{d}})=$

• A

  $17 \overline{\mathrm{i}}-15 \overline{\mathrm{j}}+9 \overline{\mathrm{k}}$
• Correct answer
  B

  $31 \overline{\mathrm{i}}-\overline{\mathrm{j}}+23 \overline{\mathrm{k}}$
• C

  $17 \overline{\mathrm{i}}-\overline{\mathrm{j}}+23 \overline{\mathrm{k}}$
• D

  $31 \overline{\mathrm{i}}-15 \overline{\mathrm{j}}+9 \overline{\mathrm{k}}$

Hence, the correct answer is option: 'B'.