All Grade 12 Calculus or Introductory Level Calculus Notes

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atCt 9 8m15
Vectors
Mathematical Quantities
Vectors quantities that have both magnitude size
and direction velocity TtCtm h W 3direction
fIdm
Scalars quantities described by magnitude only
examples temperature TC 15 C
speed IF CHI too km h

vectors
A rector can be represented by a directed line segment
Catgngistipinead 118011 magnitude
2
length
IFI 542 22 20J
the magnitude of the vector is represented by the
length of the arrow
the direction of the vector is represented by the direction
the arrow is pointing Cotten given as an angle

TERMINOLOGY
Equivalent vectors 2 vectors are equivalent or equal if
they have the same magnitude and direction location
is irrelevant

opposite Vectors 2 vectors are opposite if they have the
same magnitude but point in different directions

Parallel vectors 2 vectors are parallel if they point in
either the same or opposite directions It
Hot
I
s
181 5 12 f
I at and 50 are equivalent
Ey Fg T is oppositeto atf and 50

, vectors
all are EEE
parallel
Zero vector denoted by O the magnitude of the zen
vector is o and is the only vector w no specified
direction
COMBIN IN ING VECTORS
we often want to know the combined effect or
sum of 2 or more vectors

P 800 km h E
WI 200km h w
wit 100km In E
FY pot cut 900 km h E
V2 P T2 600km h

Wit 1000 km h W Bt pot w 200km h w

lot 100km In E 200N wit
wat 100 km h W 20N a wet
VECTOR ADAMDATIN
It a and I are vectors positioned so that the tail
of a is at the tip of u then the sum of
u tr is the rector from the tail of a to the
of 1 tip
triangle LAW
É t
jt
Ie start
y
r



F wet T T T
PARALLELOGRAM
up
a LAI Jeg E


D D
TD S