What are the patterns
The Z, F and C pattern
Cosine law
a^2=b^2+c^2-2bc cos A
vector
a quantity with both magnitude and direction
velocity, displacement, force, momentum, acceleration, torque, weight
scalar
a quantity with magnitude only
ex. speed, distance, time, mass, work, area, temperature
in a diagram, a geometric vector is represented by
a directed line segment, (otherwise
known as an ARROW)!!!
The direction
that the arrow
points is the
direction of
the
vector
The length of the
arrow is represented by
___________________
_______________, and
represents the
_______________ of
the vector. The
algebraic symbol for
this is:
the positive real number
magnitude
|V(arrow on top)|
the algebraic symbol used for a vector is
a letter with an arrow on top
Sometimes it is necessary to explicitly state the initial
point and the end point of a vector. For example, if the initial point and
end point of a vector were A and B, respectively, then we could also
refer to this vector as:
(This type of vector is called a _________________________ vector.)
point-to-point
The direction of a vector can be specified in a few different ways.
One way is to express
it as an
Alternatively, it is common to use the
angle, moving counterclockwise with respect to a horizontal line (You see this
often in physics).
angle that it makes with another
vector:
Definition: The angle between two vectors is the angle
( 180°) formed when
the vectors are placed tail to tail; that is, starting at the same point.
In navigation, vector directions are expressed as
bearings:
bearings Definition: A true bearing (or azimuth bearing) is
a compass measurement
where the angle is measured from north in a clockwise direction.
True bearings are expressed as _________________________________ ,
including leading zeros. Thus, north is a bearing of ________ , east is _______ ,
south is ______ , and west is _______.
three digit numbers
000 degrees
090 degrees
180 degrees
270 degrees
A quadrant bearing is
a measurement between 0o and 90o east or west of the north-south line.
- Two vectors are said to be EQUIVALENT if and only if ___________________
______________________________________________________________________ .
they have the same magnitude and direction
- Two vectors are said to be OPPOSITE if they have the same ________________ ,
but ___________________________________________________________________ .
When two vectors are OPPOSITE, we say that one is the ______________
of the other.
magnitude but opposite direction (angle between them is 180 degrees)
negative
- Two vectors are PARALLEL if their ________________ are the same or
opposite.
When two vectors are parallel, one of the vectors can be written in terms
of the other using _________________ ____________________________
directions
“scaler multiplication”
Two vectors u and v are parallel if and only if u= _______
Kv(arrow) where KER, k=\0
- Vector Addition
Many physical applications to vectors involve finding the combined effect,
or sum of two or more vectors.
vector AB + vector BC
= vector AC
vector r is the
resultant factor
the triangle law of vector addition
to find the sum of two vectors arrange them from tail to head
the sum is the vector
from the tail of the first vector the head of the second vector. we refer to this as the resultant.
to find the sum of two vectors arrange them from tail to head. the sum is the vector from the tail of the first vector the head of the second vector. we refer to this as
the resultant
