If the vectors $2 \overline{\mathrm{i}}+4 \overline{\mathrm{j}}-3 \overline{\mathrm{k}},-\overline{\mathrm{i}}+2 \overline{\mathrm{j}}+3 \overline{\mathrm{k}}$ and $\mathrm{p} \overline{\mathrm{i}}-2 \overline{\mathrm{j}}+\overline{\mathrm{k}}$ are coplanar, then the unit vector in the direction of the vector $9 p \bar{i}-4 \bar{j}+4 \bar{k}$ is

• A

  $\frac{1}{6}(2 \overline{\mathrm{i}}-4 \overline{\mathrm{j}}+4 \overline{\mathrm{k}})$
• B

  $\frac{1}{\sqrt{57}}(5 \overline{\mathrm{i}}-4 \overline{\mathrm{j}}+4 \overline{\mathrm{k}})$
• C

  $\frac{1}{\sqrt{68}}(6 \overline{\mathrm{i}}-4 \overline{\mathrm{j}}+4 \overline{\mathrm{k}})$
• Correct answer
  D

  $\frac{1}{9}(-7 \overline{\mathrm{i}}-4 \overline{\mathrm{j}}+4 \overline{\mathrm{k}})$

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