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Question: The points (0, –1, –1), (–4, 4, 4), (4, 5, 1) and (3, 9, 4) are...

The points (0, –1, –1), (–4, 4, 4), (4, 5, 1) and (3, 9, 4) are

A

Collinear

B

Coplanar

C

Forming a square

D

None of these

Answer

Coplanar

Explanation

Solution

Equation of the plane passing through the points

(0, –1, –1), (–4, 4, 4) and (4, 5, 1) is x(y+1)(z+1)455462=0\left| \begin{array} { c c c } x & ( y + 1 ) & ( z + 1 ) \\ - 4 & 5 & 5 \\ 4 & 6 & 2 \end{array} \right| = 0 …. (1)

The point (3, 9, 4) satisfies the equation (1)