Show that the points having position vectors `6 hat i-7 hat j ,\ 16 hat i-19 hat j-4 hat k ,\ 3 hat j-6 hat k ,\ 2 hat i+5 hat j+10 hat k` are not coplanar.

Explanation

$$ \begin{array}{ll} \vec{A}=6 \hat{\imath}-7 \hat{\imath} & \overrightarrow{A B}=10 \hat{\imath}-12 \hat{\imath}-4 \hat{k} \\ \vec{B}=16 \hat{\imath}-19 \hat{\imath}-4 \hat{k} & \overrightarrow{A C}=-6 \hat{\imath}+10 \hat{\imath}-6 \hat{k} \\ \vec{C}=3 \hat{\imath}-6 \hat{k} & \overrightarrow{A D}=-4 \hat{\imath}+12 \hat{\imath}+10 \hat{k} \\ \vec{D}=2 \hat{\imath}+5 \hat{\imath}+10 \hat{k} & \end{array} $$
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