6 The points \(A , B\) and \(C\) have position vectors \(2 \mathbf { i } - \mathbf { j } + \mathbf { k } , 3 \mathbf { i } + 4 \mathbf { j } - \mathbf { k }\) and \(- \mathbf { i } + 2 \mathbf { j } + 4 \mathbf { k }\) respectively.
- Find the area of the triangle \(A B C\).
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\includegraphics[max width=\textwidth, alt={}]{9221f480-4af6-44be-a535-d2ceb0f8b5d2-08_72_1566_484_328} ................................................................................................................................... ....................................................................................................................................
\includegraphics[max width=\textwidth, alt={}, center]{9221f480-4af6-44be-a535-d2ceb0f8b5d2-08_71_1563_772_331}
\includegraphics[max width=\textwidth, alt={}, center]{9221f480-4af6-44be-a535-d2ceb0f8b5d2-08_71_1563_868_331} - Find the perpendicular distance of the point \(A\) from the line \(B C\).
- Find the cartesian equation of the plane through \(A , B\) and \(C\).