Let E-ABCD be a pyramid on square base ABCD where A is the origin and B and D are lying on positive x-axis and positive y-axis respectively. If E is  $(0,2,3)$and  $\overrightarrow{DE}.(\widehat{i}+\widehat{j})=0$, then which of the following statement(s) is (are) correct?

$\overrightarrow{DE}.(\widehat{i}+\widehat{j})=0$

Foot of  perpendicular ot E$(0,2,3)$ on xy plane is D(0,2,0)

Plane ABE is  $\left|\begin{array}{ccc}x& y& z\\ 0& 2& 3\\ 2& 0& 0\end{array}\right|=0$

Image of D(0,2,0) in the plane 3y-2z=0 is  $(0,\frac{-10}{13},\frac{24}{13})$

Foot of perpendiuclar of D(0,2,0) on the plane 3y-2z=0 is $(0,\frac{8}{13},\frac{12}{13})$

Volume of tetrahedron ABDE=$V=\frac{1}{3}(Area of triangle ABD) height=\frac{1}{3}\left(\frac{1}{2}\left(2\right)\left(2\right)\right)3=2$