440 likes | 564 Views
MA242.003. Day 9 – January 17, 2013 Review: Equations of lines, Section 9.5 Section 9.5 –Planes. Equations of PLANES in space. Equations of PLANES in space. Different ways to specify a plane:. Equations of PLANES in space. Different ways to specify a plane:.
E N D
MA242.003 Day 9 – January 17, 2013 Review: Equations of lines, Section 9.5 Section 9.5 –Planes
Equations of PLANES in space. Different ways to specify a plane:
Equations of PLANES in space. Different ways to specify a plane: 1. Give three non-co-linear points.
Equations of PLANES in space. Different ways to specify a plane: 1. Give three non-co-linear points.
Equations of PLANES in space. Different ways to specify a plane: 2. Give two non-parallel intersecting lines.
Equations of PLANES in space. Different ways to specify a plane: 2. Give two non-parallel intersecting lines.
Equations of PLANES in space. Different ways to specify a plane: Specify a point and a normal vector
Example: Find an equation for the plane containing the point (1,-5,2) with normal vector <-3,7,5>
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
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
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>
Two lines are parallel their direction vectors are parallel when
Two lines are perpendicular their direction vectors are orthogonal when
Two planes are parallel Their normal vectors are parallel when
Two planes are perpendicular Their normal vectors are orthogonal when
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
A line is perpendicular to a plane when
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