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Equations of PLANES in space.
1. Give three non-co-linear points.
Different ways to specify a plane:
Equations of PLANES in space.
1. Give three non-co-linear points.
Different ways to specify a plane:
Equations of PLANES in space.
2. Give two non-parallel intersecting lines.
Different ways to specify a plane:
Equations of PLANES in space.
2. Give two non-parallel intersecting lines.
Different ways to specify a plane:
Equations of PLANES in space.
Different ways to specify a plane:
3. Specify a point
and a normal vector
Example: Find an equation for the plane containing the the points P=(1,-5,2), Q=(-3,8,2) and R=(0,-1,4)
The Geometry of Lines and Planes
• For us, a LINE in space is a
Point
and a direction vector v = <a,b,c>
The Geometry of Lines and Planes
• For us, a Plane in space is a
Point on the plane
And a normal vector n = <a,b,c>
A line is parallel to a plane
when
the direction vector v for the line is orthogonal to the normal vector n for the plane
A line is perpendicular to a plane
when
the direction vector v for the line is parallel to the normal vector n for the plane