If `veca, vecb and vecc` are any three non-coplanar vectors, then prove that points `l_(1)veca+ m_(1)vecb+ n_(1)vecc, l_(2)veca+m_(2)vecb+n_(2)vecc, l_(3)veca+m_(3)vecb+ n_(3)vecc, l_(4)veca + m_(4)vecb+ n_(4)vecc` are coplanar if `|{:(l_(1),, l_(2),,l_(3),,l_(4)),(m_(1),,m_(2),,m_(3),,m_(4)), (n_1,,n_2,, n_3,,n_4),(1,,1,,1,,1):}|=0`

Explanation

To prove that the points \( l_1 \vec{a} + m_1 \vec{b} + n_1 \vec{c}, l_2 \vec{a} + m_2 \vec{b} + n_2 \vec{c}, l_3 \vec{a} + m_3 \vec{b} + n_3 \vec{c}, l_4 \vec{a} + m_4 \vec{b} + n_4 \vec{c} \) are coplanar if the determinant

\[
\begin{vmatrix}
l_1 & l_2 & l_3 & l_4 \\
m_1 & m_2 & m_3 & m_4 \\
n_1 & n_2 & n_3 & n_4 \\
1 & 1 & 1 & 1
...