Lets Learn Lines and Planes in 3-Dimension!

The angle between 2 lines

We define the angle between 2 lines to be the angle between their direction vectors placed tail to tail. Notice that this definition works equally well if the lines don't actually cut each other since we then just slide the 2 direction vectors together until their tails meet.

Ways to find the angle between two lines.

The angle between 2 planes

  

• Two planes intersect at a straight line. This line is known as the line of intersection.

• The angle between two planes that intersect is the angle between two lines, one on each planes, that is perpendicular to the line of intersection and from a common point on the line of intersection.

•  Line of intersection = two same letters of the two planes.

                                                     

                     Angle between lines and planes

                                       

                                                     

 

•  A normal to a plane is a straight line that is perpendicular to any line on the plane that     passes through the intersection point of the straight line and the plane.

• The orthogonal projection is the line joining the normal vertex on the plane to the other vertex of the line on the plane.

• The angle between a line and a plane is the angle between the line and its orthogonal projection on the plane.

                                                         

                                           

               

DONE BY,

Adina.