Premium Only Content

Problems Plus 3: Line and Surface of Two Intersecting Planes
In this video I determine the symmetric equations of a line at the intersection of two planes. I then find out that when the equations of the plane vary, the line sweeps out a circular hyperboloid of one sheet. Finally, I calculate the volume of this surface between two planes.
Timestamps:
- Problem 3: Intersecting planes: 0:00
- Solution to (a): Symmetric equations for L: 1:07
- Finding a point on both planes: 1:52
- Obtaining normal vectors of the planes: 5:20
- Cross product of normal vectors is parallel to L: 7:14
- Obtain symmetric equations of L: 13:02
- Symmetric equations of L formula: 15:30
- Case where c = 0: 16:53
- Case where c = -1: 18:18
- Case where c = 1: 20:54
- Graphing with GeoGebra: 22:52
- Solution to (b): Curve of intersection: 28:16
- Solving y and x in terms of c and t: 30:34
- Eliminating c by finding squares of x and y: 36:15
- Obtain a trigonometric identity: 39:26
- Using trigonometric identity to eliminate c: 40:20
- Obtain a circle: 44:26
- Graphing in GeoGebra shows a hyperboloid of one sheet: 45:11
- Solution to (c): Volume of the hyperboloid: 49:26
- Volume is integral of area = 4/3 pi: 52:21
Video notes and playlists:
- HIVE notes: https://peakd.com/hive-128780/@mes/jlgigkdl
- Full video and playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0G_7Jd6ZORHFQMk8jbwmkos
- Vectors and the Geometry of Space playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
------------------------------------------------------
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: contact@mes.fm
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
-
2:13:07
Math Easy Solutions
17 days ago $0.01 earnedMES Math Q/A 27: What is Ball Lightning?
1931 -
17:14
GritsGG
16 hours agoSolo Warzone Victory! Rank 1 Player Dominates Lobby!
9.95K1 -
11:25
Nikko Ortiz
3 days agoMost Painful Fails
90.6K41 -
Omar Elattar
8 months agoHow I Went to Prison TWICE... then Built a $36 Million Empire - Ryan Stewman
10.5K5 -
4:50:26
Akademiks
11 hours agoLebron DUCKS Drake at Toronto 'Caribana'. Rah Ali vs Cardi B? is OTF Vonni Snitching on Durk?
68.1K9 -
10:09:48
SpartakusLIVE
14 hours ago#1 Saturday Spartoons
164K3 -
58:56
The Connect: With Johnny Mitchell
17 hours ago $21.56 earnedA Migrant Smuggler Reveals How Cartel Trafficking Works, WARNS Of Conditions At The Border
60K26 -
2:24:56
The Quartering
11 hours agoThe Final Boss! Expedition 33
77.7K4 -
24:31
Liberty Hangout
5 days agoDeranged Democrats Go Insane
81.4K215 -
11:43:10
FusedAegisTV
1 day agoOFFICIAL Evo 2025 Day 2 Co-Stream - Las Vegas, NV ∥ 14,000+ Entrants! & Top 24s
114K2