Title: Theory / Unimportant / Experimental / Physics / Introduction to Mechanic - Kleppner, Kolenkow / 1 Vectors
Tags: toBinaryFunction hasSeenConjDef

Name: A vector
Definition: A directed line segment (independant from its exact poisition)
Page: 2
Chapter: 1
Section: 2.1
Denoted by: \(\vec A\), \(\mathbf A\)
Representation: an arrow, showing both its scale length and its direction

Definition: The magnitude of \(\mathbf A\)
Page: 3
Chapter: 1
Section: 2.1
Variables: \(\mathbf A\) a vector
Context: physics
Notation: [$]\abs{\mathbf A}[/$]
Notation2: \(A\)

Name: A unit vector
Definition: A vector of magnitude 1
Page: 3
Chapter: 1
Section: 2.1

Definition: \(\frac{\mathbf A}A\)
Page: 3
Chapter: 1
Section: 2.1
Variables: \(\mathbf A\) a vector
Notation: \(\hat{\mathbf A}\)

Definition: The vector with direction of \(\mathbf A\) and \(b\) time its magnitude
Page: 3
Chapter: 1
Variables: \(\mathbf A\) a vector
\(b\) a scalar
Notation: \(b\mathbf A\)
Assuming: \(b>0\)

Definition: The vector with direction inverse of \(\mathbf A\) and \(-b\) time its magnitude
Page: 3
Chapter: 1
Variables: \(\mathbf A\) a vector
\(b\) a scalar
Notation: \(b\mathbf A\)
Assuming: \(b<0\)

Page: 3
Notation: \(\mathbf A+\mathbf B\)
Variables: \(\mathbf {A,B}\) a vector
Chapter: 1
Definition: The vector, obtained when the tail of \(\mathbf B\) is drawn at the head of \(\mathbf A\)
Associative: Group operation, distributive for multiplication by a scalar

Definition: \(\mathbf A+(-1)\mathbf B\)
Page: 3
Chapter: 1
Variables: \(\mathbf {A,B}\) a vector
Notation: \(\mathbf A-\mathbf B\)

Page: 3
Section: 4.1
Notation: \(\mathbf A\cdot\mathbf B\)
Variables: \(\mathbf {A,B}\) a vector
Chapter: 1
Name: Scalar product of \(\mathbf A\) and \(\mathbf B\)
Definition: \(AB\cos\theta\), with \(\theta\) the angle between \(\mathbf A\) and \(\mathbf B\) if they are nonzero. 0 otherwise
Commutative: Commutative
Name2: Dot product of \(\mathbf A\) and \(\mathbf B\)

Question: The equation relating A B C and an angle
Answer: \(C^2=A^2+B^2-2AB\cos\phi\)
Page: 5
Chapter: 1
Section: 4.1
Kind: Ex

Page: 6
Section: 4.2
Notation: \(\mathbf A\times\mathbf B\)
Variables: \(\mathbf A,\mathbf B\) vectors
Chapter: 1
Name: The vector product of \(\mathbf A\) and \(\mathbf B\)
Definition: magnitude \(AB\sin\theta\) with \(\theta\) the angle between \(\mathbf A\) and \(\mathbf B\)
Kind: Ex
Commutative: Anticommutative
Intuition: Take the parallelogram \(P\) with side \(\mathbf A\) and \(\mathbf B\).
This product's magnitude is the area, and the direction is normal to \(P\)
Definition2: direction perpendicular to the plane \(\mathbf A,\mathbf B\), with \(\mathbf {A,B,C}\) a right-hand triple
ConjDef: both
Name2: \(\mathbf A\) cross \(\mathbf B\)

Question: \(\mathbf A\times\mathbf A\)=
Answer: 0
Page: 6
Chapter: 1
Section: 4.2
Variables: \(\mathbf A\) vectors
Kind: Ex

Name: A right-hand triple
Definition: Three vectors \(\mathbf {A,B,C}\) such that if \(\mathbf A\) lies on the \(x\) axis, \(B\) lies towards the \(y\) axis,\(\mathbf C\) lies along the positive \(z\) axis.
Page: 6
Chapter: 1
Section: 4.2

Question: \(-\mathbf {A\times B}\) equals
Answer: \(\mathbf {B\times A}\)
Page: 6
Chapter: 1
Section: 4.2
Variables: \(\mathbf A,\mathbf B\) vectors

Name: An anticommutative operation
Definition: An operation \(\cdot\) such that \(a\cdot b=-b\cdot a\)
Page: 6
Chapter: 1
Section: 4.2

Name: Analytic geometry
Definition: Combination of algebra and geometry
Page: 8
Chapter: 1
Section: 5