Base of a pyramid is rectangular, three of its vertices of the base are A (2, 2, $-1$) B(3, 1, 2)  and C (1, 1, 1) and its vertex at the top is  $P(4,\frac{-26}{3},\frac{-10}{3})$ . Fourth vertex of the base is D. Which of the following statements is (are) CORRECT?

 $P(4,\frac{-26}{3},\frac{-10}{3})$
 $\overline{AB}=\widehat{i}+\widehat{j}+3\widehat{k},\overline{AC}=-\widehat{i}-\widehat{j}+2\widehat{k},\overline{BC}=-2\widehat{i}-\widehat{k}$
 $\overline{AC}\perp \overline{BC}$
 
 $\frac{A+B}{2}=\frac{C+D}{2}\Rightarrow D=(4,2,0)$
Equation of plane through A, B, C, D is  $x-5y-2z+6=0$
foot of perpendicular drawn form P is (h, k, r)
 $\frac{h-4}{1}=\frac{k+\frac{26}{3}}{-5}=\frac{r+\frac{10}{3}}{-2}=\frac{-(4+\frac{130}{3}+\frac{20}{3}+6)}{30}$
 $\Rightarrow (h,k,r)=(2,\frac{4}{3},\frac{2}{3})=(\mathcal{l},m,n)$
$\mathcal{l}+m-2n=2, \mathcal{l}>m>n$ 
volume of pyramid  $=\left(\frac{1}{3}\right)$ (Base Area) (height)
$=\left(\frac{1}{3}\right)\left(\sqrt{30}\right)\left(\sqrt{120}\right)=20$  cubic units