Geometry

# 3D Coordinate Geometry - 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: $\begin{array}{c}&(0,-2,3),&&(1,0,1),&&(-1,-1,0)\end{array}$ 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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