Show that the four points `(0,-1,-1),(-4,4,4),(4,5,1)a n d(3,9,4)` are coplanar. Find the equation of plane containing them.

Explanation

To show that the four points \( A(0, -1, -1) \), \( B(-4, 4, 4) \), \( C(4, 5, 1) \), and \( D(3, 9, 4) \) are coplanar, we can use the concept of vectors and the scalar triple product. If the scalar triple product of the vectors formed by these points is zero, then the points are coplanar.

**Step 1: Find the vectors AB, AC, and AD.**

The vectors can be calculated as follows:

\[
\vec{AB} = B - A = (-4 - 0, 4 - (-1), 4 - (-1)) = (-4, 5, 5)
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