6 Find the equations of the planes that passes through three points.

   (a)      (1, 1, – 1), (6, 4, – 5), (– 4, – 2, 3) 

Answers (1)

The equation of the plane which passes through the three points A(1,1,-1),\ B(6,4,-5),\ and\ C(-4,-2,3)  is given by;

Determinant method,

\begin{vmatrix} 1 &1 &-1 \\ 6& 4 & -5\\ -4& -2 &3 \end{vmatrix} = (12-10)-(18-20)-(-12+16)

Or, = 2+2-4 = 0

Here, these three points A, B, C are collinear points.

Hence there will be an infinite number of planes possible which passing through the given points.

 

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