What is the equation of the plane passing through the points ndash 2 6 ndash 6 ndash 3 10 ndash 9 an...........

Mathematics (NDA) Coordinate Geometry

What is the equation of the plane passing through the points (–2, 6, – 6), (–3, 10, – 9) and (–5, 0, – 6)?

2x – y – 2z = 2

2x + y + 3z = 3

x + y + z = 6

x – y – z = 3

Equation of plane is
$\begin{vmatrix} x+2 &y+6 &z+6 \\ -1 &4 & -3\\ -3 & -6 & 0 \end{vmatrix}=0$

⇒(z+6)(18)+3[−6(x+2)+3(y−6)]=0
⇒18z+108+3(−6x−12+3y−18)=0

=> 2x−y−2z=2

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