Example 6: Curve of Intersection of a Cylinder and Plane
In this video I go over an example on determining the vector function of the curve of intersection between a vertical cylinder and a slanted plane. I first find an equation of the intersection by plugging the equation of the plane into the equation of the cylinder. I then determine 4 points of intersection and manually graph it out, obtaining an ellipse. Projecting this ellipse onto the x-y plane obtains a unit circle of radius 1. By using the Pythagorean Identity, I obtain parametric equations of the circle as trigonometric functions for x and y. By plugging the y parametric equation into the plane equation, we obtain the z parametric equation. From here we can combine the parametric equations into a vector function. Note that earlier in the video, I also graphed the plane and cylinder in GeoGebra 3D graphing calculator: https://www.geogebra.org/calculator/v7ecchdb
#math #3D #geogebra #science #calculus
Timestamps
- Example 6: Curve of Intersection: 0:00
- Graphing the cylinder and plane in GeoGebra: 0:20
- Equation at intersection: 1:23
- 2 Points of intersection when x = 0: 2:37
- 2 Points of intersection when x = +/- 1: 5:13
- Graphing out points of intersection: 7:23
- Better illustration of the intersection points from my Calculus book: 9:50
- Projection of the intersection curve onto x-y plane is a circle: 10:56
- Getting parametric equations of a circle via the Pythagorean Identity: 11:46
- Converting plane equation into trigonometric version: 13:26
- Parametric equations for the intersection curve: 14:27
- Corresponding vector equation of the intersection curve: 15:00
- Arrows on the curve indicate how the curve is traced as the parameter t increases: 16:03
- Parameter t is the angle going counterclockwise from the positive x axis: 17:16
Notes and playlists
- Summary: https://inleo.io/threads/view/mes/re-leothreads-skxajmlt
- Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GwdMY-E9_4LsmYmO-IxcoX
- Notes: https://peakd.com/hive-128780/@mes/omhbcxkw
- Vector Functions playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HQl7xTQBS_O8Te8PcpNm4U .
Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
MES Links: https://mes.fm/links
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes
Email me: [email protected]
Free Calculators: https://mes.fm/calculators
BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm
Free Online Tools: https://mes.fm/tools
iPhone and Android Apps: https://mes.fm/mobile-apps
▶️ 3Speak
Congratulations!
✅ Good job. Your post has been appreciated and has received support from CHESS BROTHERS ♔ 💪
♟ We invite you to use our hashtag #chessbrothers and learn more about us.
♟♟ You can also reach us on our Discord server and promote your posts there.
♟♟♟ Consider joining our curation trail so we work as a team and you get rewards automatically.
♞♟ Check out our @chessbrotherspro account to learn about the curation process carried out daily by our team.
🏅 If you want to earn profits with your HP delegation and support our project, we invite you to join the Master Investor plan. Here you can learn how to do it.
Kindly
The CHESS BROTHERS team
Congratulations @mes! You have completed the following achievement on the Hive blockchain And have been rewarded with New badge(s)
Your next target is to reach 52500 replies.
You can view your badges on your board and compare yourself to others in the Ranking
If you no longer want to receive notifications, reply to this comment with the word
STOP