Geometry

3D Coordinate Geometry

3D Coordinate Geometry - Equation of a Plane

         

What is the equation of the plane which contains the following two parallel lines: x+16=y27=z and x36=y+47=z1? \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 x3=y43=z22x-3=\frac{y-4}{3}=\frac{z-2}{-2} at (2,1,4)?(2,1,4)?

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

Which of the following is the equation of the xyxy-plane?

What is the normal vector of the following plane: x23+y+33+z54=0?\frac{x-2}{-3}+\frac{y+3}{3}+\frac{z-5}{4}=0\text{?}

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