chapter eight vocabulary Flashcards
memorize the vocabulary associated with vectors (23 cards)
vectors, the basics
some quantities have both a magnitude (numerical value) and a direction and
therefore cannot be represented by a single real number. such quantities can be
represented by a __________.
think pretty quick, its just a line.
8.1 intro into vectors
vector
a quantitiy that has an initial point and a terminal point.
8.1 intro into vectors
vectors, the basics
what are the characteristics of a vector?
think of points on a line, it has a ____ and a ____.
8.1 intro into vectors
a vector has an initial point and a terminal point. they additionally each have a magnitude and a direction.
the initial point, P, and the terminal point, Q.
8.1 intro into vectors
vectors, the basics
what notation is used to represent vectors?
think pretty quick, its just a line.
8.1 intro into vectors
the letters “PQ” and “V” with a half arrow on top. additionally notated by a bolded v.
a bolded v and a “V” with a half arrow on top is used the most.
8.1 intro into vectors
vectors, the basics
what is magnitude?
think how big. what was the magnitiude of your walk?
8.1 intro into vectors
represented by |v|, it is the distance.
remember, the v could be bolded or have a half arrow on top.
8.1 intro into vectors
vectors, the basics
the is the equation for magnitude?
think again, how much? how far was your walk?
8.1 intro into vectors
the distance formula is used.
d = √(x2 - x1) ^2 + (y2 - y1) ^2
8.1 intro into vectors
vectors, the basics
what is direction?
think where you are going.
8.1 intro into vectors
it is similar to slope.
direction = y2 - y1 / x2 - x1 (RISE OVER RUN!)
8.1 intro into vectors
vectors, the basics
when are vectors equal?
think magnitude and direction.
8.1 intro into vectors
vectors are equal if, **AND ONLY IF **, they have the same magnitude and direction.
vectors are equal if their characteristics are the same.
8.1 intro into vectors
vectors, the basics
how many vectors are equivelant to v?
do not over think it. this is math, what is the most likely answer?
8.1 intro into vectors
there are infinitely many vectors
equivalent to v. v is the most convenient vector to use to represent these vectors since its initial point is at the origin.
v has an infinate amount of equivelants.
8.1 intro into vectors
vectors, the basics
____ vectors have the same or opposite direction.
think of the different types of lines and vectors.
8.1 intro to vectors
parallel
they never touch, so the direction does not matter.
8.1 intro to vectors
vectors, the basics
____ vectors have the same magnitude but different directions.
think of the different types of lines and vectors.
8.1 intro to vectors
opposite
they are the same distance but different directions make them opposite.
8.1 intro to vectors
vectors, the basics
how do you look at opposite vectors?
think, what makes a pair negative?
8.1 intro to vectors
-(x, y)
the negative turns the pair into an opposite vector.
8.1 intro to vectors
vectors, the basics
quantities which have magnitude ONLY are known as ____.
Southern California Association for Language Assessment Research.
8.1 intro to vectors
scalar
is there a direction? if not, its a vector!
8.1 intro to vectors
vectors, the basics
what is the quantity, if a sprinter is running 100 meters north?
look at what characteristics are present!
8.1 intro to vectors
vector
both magnitude and direction are present, making it a vector.
8.1 intro to vectors
vectors, the basics
what is the quantity, if a tennis ball is served at 110 mph?
look at what characteristics are present!
8.1 intro to vectors
scaler
only the magnitude is present, making it a scaler.
8.1 intro to vectors
resultants and bearings
the sum of two or more vectors is known as the ____.
think, what is the result of adding two or more vectors together?
8.1 intro to vectors
resultant
it is the resulting remainder.
8.1 intro to vectors
resultants and bearings
what are the two methods to find the resultant?
what shapes do they create?
8.1 intro to vectors
the triangle method and the parallelogram method.
parallelogram is easier for you!
8.1 intro to vectors
resultants and bearings
how do you use the triangle method to find the resultant?
use the variables a and b.
8.1 intro to vectors
you translate b so that the tail of b touches the tip of a. the resultant is the vector from the tail of a to the tip of b.
think tip to tail.
8.1 intro to vectors
resulatants and bearings
how do you use the parallelogram method to find the resultant?
use the variables a and b.
8.1 intro to vectors
you translate b so that its tail touches the tail of a. you then complete the parallelogram so that it has two sides, and the resultant is the vector that forms on the diagonal of the parallelogram.
think tail to tail.
8.1 intro to vectors
resultants and bearings
where are quadrantal bearings usually located?
think quadrants.
8.1 intro to vectors
it will always be between 0 ≤ θ ≤ 90.
specific quandrants. start at the beginning direction and so forth.
8.1 intro to vectors
resultants and bearings
what is the characteristic of a true bearing?
not just quadrantal.
8.1 intro to vectors
it will always clockwise from north.
always start at the vertical line, or the y axis.
8.1 intro to vectors
rectangular components
when are rectangular components used?
think of specific vectors.
8.1 intro to vectors
it is used with 1 vector.
it is used to find one side!
8.1 intro to vectors
rectangular components
in rectangular components, what is the vertical component?
think of trigonometry.
8.1 intro to vectors
sin
think of finding the side of a trigangle from the origin!
8.1 intro to vectors
rectangular components
in rectangular components, what is the horizontal component?
think of trigonometry.
8.1 intro to vectors.
cos
think of finding the side of a trigangle from the origin!
8.1 intro to vectors
