Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ be three non-zero, non-coplanar vectors and $\overrightarrow{p},\overrightarrow{q},\overrightarrow{r}$ be three vectors given by $\overrightarrow{p}=\overrightarrow{a}+2\overrightarrow{b}-2\overrightarrow{c}, \overrightarrow{q}=3\overrightarrow{a}+\overrightarrow{b}-3\overrightarrow{c}$ and $\overrightarrow{r}=\overrightarrow{a}-4\overrightarrow{b}+4\overrightarrow{c}.$ If the volume of parallelepiped determined by $\overrightarrow{a}, \overrightarrow{b}$ and $\overrightarrow{c}$ is $v_1$ cubic units and volume of tetrahedron determined by $\overrightarrow{p}, \overrightarrow{q}$ and $\overrightarrow{r}$ is $v_2$ cubic units, then $\frac{v_1}{v_2}$ is equal to

• A

  $\frac{1}{3}$
• B

  $\frac{3}{4}$
• C

  $\frac{1}{4}$
• Correct answer
  D

  $\frac{1}{2}$

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