Application to this would be finding distance from point to plane and finding angle between 2 planes. A. Distance point-plane: 1. Let P and Pi be the point and plane that you want to find the distance between 2. Find the normal line N just like in my comment below (call the intersection of L and N as point O) 3. Make a line from P to line N (call it's intersection P'), call that line PP' 4. Connect P' and O 5. Distance(P, Pi) = Distance(P', O) 6. Copy P'O line to find the distance line of P to Pi (optional, just for visualization of what we want to achieve in the beginning, you can also use this line to find the distance between point and line) This can also be applied to distance between line and plane, because the only way it's possible is if the line is parallel to the plane and you can pick any point from that line to the plane to find the distance. B. Angle between 2 planes (call it Pi1 and Pi2): 1. Find the normal lines of those two planes (call it N1,N2) 2. Angle(Pi1,PI2) = Angle(N1,N2) (what i mean by angle here is the acute angle, not obtuse. If you find N1 and N2 to be skew to each other just joint them together in a same point)
Here's how to do the inverse of the last example in this video (finding normal line of a plane angled against x,y,z axis): 1.Let the plane that you want to find the normal line called pi 2. Look parallel along the trace line of pi in the horizontal plane (xy plane) we will call that line t1 3. t1 is the normal line of a plane (just like the yellow plane in 11:36) we will call that plane pi1 (this plane has no inclination against the z axis so it's easier to find the normal line of it) 4. Intersect pi and pi1 and call the line L, then just find the line perpendicular to L to find the normal line to pi (call that N, this last part works to find the normal line because we were looking at the plane as an edge and looking perpendicular to the shadow of N, thus giving us the direction of N) i dont know how to find the true length of N though, but just the direction is already important enough
during online class this video is very helpful.
YOU GUYS SHOULD PUT ALL THE VIDEOS THAT DEAL WITH DESCRIPTIVE GEOMETRY IN ITS OWN PLAY LIST
HI Joshua, All the videos are organised according to topic on our class website.
www.gmitletterfrackresourcecentre.com/techncial-graphics.html
Application to this would be finding distance from point to plane and finding angle between 2 planes.
A. Distance point-plane:
1. Let P and Pi be the point and plane that you want to find the distance between
2. Find the normal line N just like in my comment below (call the intersection of L and N as point O)
3. Make a line from P to line N (call it's intersection P'), call that line PP'
4. Connect P' and O
5. Distance(P, Pi) = Distance(P', O)
6. Copy P'O line to find the distance line of P to Pi (optional, just for visualization of what we want to achieve in the beginning, you can also use this line to find the distance between point and line)
This can also be applied to distance between line and plane, because the only way it's possible is if the line is parallel to the plane and you can pick any point from that line to the plane to find the distance.
B. Angle between 2 planes (call it Pi1 and Pi2):
1. Find the normal lines of those two planes (call it N1,N2)
2. Angle(Pi1,PI2) = Angle(N1,N2) (what i mean by angle here is the acute angle, not obtuse. If you find N1 and N2 to be skew to each other just joint them together in a same point)
Here's how to do the inverse of the last example in this video (finding normal line of a plane angled against x,y,z axis):
1.Let the plane that you want to find the normal line called pi
2. Look parallel along the trace line of pi in the horizontal plane (xy plane) we will call that line t1
3. t1 is the normal line of a plane (just like the yellow plane in 11:36) we will call that plane pi1 (this plane has no inclination against the z axis so it's easier to find the normal line of it)
4. Intersect pi and pi1 and call the line L, then just find the line perpendicular to L to find the normal line to pi (call that N, this last part works to find the normal line because we were looking at the plane as an edge and looking perpendicular to the shadow of N, thus giving us the direction of N)
i dont know how to find the true length of N though, but just the direction is already important enough