The four points with position vectors $3\overrightarrow{i}+5\overrightarrow{j},3\overrightarrow{j}-5\overrightarrow{k},5\overrightarrow{i}-19\overrightarrow{j}-3\overrightarrow{k}$ and $6\overrightarrow{i}-5\overrightarrow{j}$

Consider the points as A, B, C and D

$\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}=-3\overrightarrow{i}-2\overrightarrow{j}-5\overrightarrow{k}$

$\overrightarrow{AC}=\overrightarrow{OC}-\overrightarrow{OA}=2\overrightarrow{i}-24\overrightarrow{j}-3\overrightarrow{k}$

$\overrightarrow{AD}=\overrightarrow{OC}-\overrightarrow{OA}=3\overrightarrow{i}-10\overrightarrow{j}$

Consider $\left|\begin{array}{ccc}-3& -2& -5\\ 2& -24& -3\\ 3& -10& 0\end{array}\right|$

$=-3(0-30)+2(0+9)-5(-20+72)$

$=-152\ne 0$

Given vectors are L.I