Summary
Zusammenfassung Ebenen
- Course
- Institution
Strukturierter Lernzettel zum Thema Ebenen.Sorgt für Motivation.
[Show more]
Seller
Follow
larascholz
Content preview
EbenenNormalenform der Ebene Abstand eines Punktes von einer Ebene
->
H. F.esvektor iIrä -
?)
-
d -7
Tvormalenvektor
=
(2)
U
Punkt-Richtungs-Form einer Ebene Hessesche Normalenform Koordinatengleichung der Ebene
ax
by
+
cz d 0
+ +
=
~Ortsvektor no.( ri) - 0
=
F(X,M) F x.a u. =
+ +
Fiat ânors o
RU nichtkollinear Abstand zweier paralleler Ebenen
En:2x 4y 3z 12
Schnittwinkel zwischen zwei Ebenen
+
- =
Drei-Punkte-Form einer Ebene E2:
-
6x 12y 9z
-
30
cos). (
-
+ =
1 =
F(X,M) F =
x.( )
+
-
m.(r r)
+ -
d1 -
(.dz
d =
s
Ortsvektoren
Schnitt zweier Ebenen Schnitt Gerade - Ebene
E +
x. r x2. =
+
Mc
+
.52
Fi x1a n.5
+
+
r xz.a2 Mz.52
=
+ +
keine Lösung: Die Gerade liegt parallel zur Ebene
keine Lösung: Die Ebenen liegen parallel. eine Lösung: Ein Schnittpunkt existiert.
Die Normalenvektoren sind kollinear.
unendlich viele Lösungen: Die Gerade liegt in der Ebene.
unendlich viele Lösungen, 1 freier Parameter:
Es existiert eine Schnittgerade.
Die Normalenvektoren sind nicht kollinear.
Die Richtung der Schnittgeraden entspricht dem Schnittwinkel zwischen Ebene und Gerade
Vektorprodukt der Normalenvektoren.
7 90° cos) E: (
unendlich viele Lösungen, 2 freie Parameter:
= -
Die Ebenen sind identisch.
Die Normalenvektoren sind kollinear.
Normalenform in Koordinatenform
Abstand Ebene - zu einer zur Ebene parallelen Gerade Er: (2).((l)-18) 0
=
E: (a) s.(-2) t.) 2)
=
+ +
-
( (-).(28)
= 0
=
9: = (-
) r.(E) +
22 = -
2.(X 6) -
+
1/y
-
7) 2.1z +
-
8) 0
=
E:
-
4x 2y z
-
8 2 3 7
2x 12 y 2z
+ +
16
=
0
= -
+ - +
+ -
=
HNF:
7
E,: 2x y 2z 11 0
- =
= + -
+
-
4.2 2.1 478 + -
2
-
21
21
Normalenform in Parameterform
E:((((?) (2)) - =
0
Koordinatenform in Parameterform Parameterform in Normalenform (i) ==(ül
n ()
=
=
E: 2x y 2z 11
(8) r.(8) s.() =: (2) r.(9) s.()
- +
+
=
=:=
+
+
+
= +
1 1010)
-
A
(3 (8) (3%
=
x
=
n =
B
= 1011110)
c 10181 =)
(8.((2) (81)
=
-
0
=
=:
(8)
=:=
r.(+ s. Koordinatenform in Normalenform
+
E:3x
2y 2z 6
=
+ +
Parameterform in Koordinatenform E: (2)(12) (8)) -
0
=
3x 2.0 +
2.0 0
=
(8) r.(8) s.()
+
=:=
+
+
x 2
=
n (3 (8) (3%
=
x
=
E: 18x 6y
=
+
d
18.2 6.8 0 d
=
+
+
36 d
=
36
E: 18x
6y
=
+
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller larascholz. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $5.97. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
64438 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now