Question

Find the equations of the planes that passes through $$(1,1,-1),(6,4,-5),(-4,-2,3)$$

Solution

The given points are $$A(1,1,-1), B(6,4,-5)$$ and $$C(-4,-2,3)$$.$$\begin{vmatrix} 1 & 1 & -1 \\ 6 & 4 & -5 \\ -4 & -2 & 3 \end{vmatrix}=(12-10)-(18-20)-(12+16)=2+2-4=0$$$$\Rightarrow$$ Points are collinear. Since $$A, B, C$$ are collinear points, there will be infinite number of planes passing through the given points.MathematicsRS AgarwalStandard XII

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