Angles
Angles between a Line and a Plane
From the applet above, can you derive how to find the angle between a line and a plane. Explain the key elements of this formula.
Angles between two Planes
Derive the equation for the angle between two planes.
You can vary the sliders for [math]d[/math] and [math]f[/math] (the constants in the equation of the plane), what does this do in order to explain why we consider the normals of planes.
The applet has tools there to help you with questions a-c, for the rest, you will need to add other elements. The following commands will help, as you start to type, press the correct option:[br]- Vector (point)[br]- Line (Point, Direction)[br]- Cross (vector, vector)[br][br]You can also use the tools at the top to find angles between vectors, or lines
In part d) you discussed the direction of the line of intersection between two planes, can you explain why the line of intersection moves in the direction of the cross product of the normals to each of the planes?