This course covers all major topics in MAM1000W, such as derivatives and integration, the applications thereof, matrices, vectors and so forth. Provided are documents of "cheat sheets" with the introduction and in-depth derivation of a topic , as well as the outlines of the specific equations, when...
VECTORS
A vector is a quantity that hasboth magnitudeanddirection
Examples are force displacement and acceleration
GEOMETRIC DESCRIPTION OF VECTORS
Suppose a particle moves along a line segment from A to B thevector y has
an initial point A thetail andterminal point B the tip and we indicate thisby
writing I AB
7
He can also combine two vectors AB and BE to have the resultantvector
AT
É To get to point c from A we can movefrompoint A
g to B with vector AB and from point B to point Cwith
vector BE
A AB Bc Ad
We now define Yeater Addition and Scalar multiplication
VECTOR ADDITION
If i and I are vectors positioned so the initialpointoff is at the terminal
ut
thenthesum Itf is the vector from the initial point of it totheterminal
port
of f
Triangle Law
II Parallelogram Law
some represent
vector P and I
SCALARMULTIPLICATION
If c is a scalar and I vector then the scalarmultiple of is thevector
whose length is c times thelength of t andwhose direction is thesameas I
it c o and is opposite to 7 if Cao
vector
If c o or to cry on The zero
, I In E É
we can now define difference of 2 vectu
DIFFERENCE OF TWO VECTORS
É T at Cf Its basically vector Addition of it and opposite
directionof F
i Est
II n
our path
COMPONENTS OF A VECTOR
If the initialpoint of a vector at at the origin of a rectanglecoordia
we place
vector at has coordinates of the form
system then the point of a
terminal
9,9
or Ca 92,93 if 30
These coordinates are called
components of a and we conte
at ya ya or at 9,9293
ya Callan
Ca ar93
n
o z
at La y
an
y
a a 92,937
Given thepoints ACK y Z and B ka gu ta the vectra with respresentation
AB is a ka ki yo y Zz t
MAGNITUDE OF A VECTOR
If a a asas then the length of a at a taita
A unitvector is avectorwithmagnitude of 1 an a as as is a unitvector
aptaita
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