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3D Coordinate Geometry

Append a z-axis to the 2-dimensional plane and conquer the realm of 3-dimensional space.

Equation of a Plane

What is the equation of the plane which contains the following two parallel lines: \[ \frac{x+1}{6} = \frac{y-2}{7} = z \hspace{.3cm} \text{ and } \hspace{.3cm} \frac{x-3}{6} = \frac{y+4}{7} = z-1?\]

What is the equation of the plane that meets perpendicularly with the line \[x-3=\frac{y-4}{3}=\frac{z-2}{-2}\] at \((2,1,4)?\)

The equation of the plane that passes through the three points: \[\begin{array}&(0,-2,3),&&(1,0,1),&&(-1,-1,0)\end{array}\] is \(ax+by+cz+1=0.\) Find the value of \(a+b+c.\)

Which of the following is the equation of the \(xy\)-plane?

What is the normal vector of the following plane: \[\frac{x-2}{-3}+\frac{y+3}{3}+\frac{z-5}{4}=0\text{?}\]

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