×

## 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: $\frac{x-2}{-3}+\frac{y+3}{3}+\frac{z-5}{4}=0\text{?}$

×

Problem Loading...

Note Loading...

Set Loading...