vectors math quiz
the vector equation of a line is ——-. a-> is the ——- of a point. b-> is the ——- thats —— to the line. this is called the ——. in the end, column form (x y) turns into ——
(x y) column form = a-> + (t)(b->), position vector, vector, parrellel to, direction vector, coordinates (x,y)
when doing the dot product of the number and there is a missing variable sub it in as ——
0
a unit vector is a vector that is —— long. in order to find the unit vector, you take the ——— values and turn it into a —- with the denominator being the ——-
1 unit long, component form values, fraction, length
a position vector is represented like ——-
OP ->
vectors are parrellel when they are in the —- or —— —-. however, parallel vectors have ——
same or opposite direction, different magnitudes
when observing individual points using the vector equation, it may be helpful to look at the equation like
a-> + tb->
you can numerically —— and ——— vectors, as well as ——— them
add subtract, mult divide
a vector indicated direction with ——, and it has ——
arrows endpoints
column form is represented ———, while component form is represented with ——-
between parentheses, i and j
the two ways to numerically represent a vector are in. ——- and ——-
component form and column form
angle equation is ———. in order to solve this the final step is to do ——. when plugging the two bottom roots into the calculator, just do the square root of the ——-
cos (-)= v •w / |v| |w|, cos^-1, two multiplied together
a vector is a ——- —— —— which is used to represent a ——- ——
directed line segment, vector quantity
a displacement vector represents the —- and —- of the most —- —- between ——
direction and magnitude, direct path between two points
a vector quantity has both —— and ——. some examples of vectors in the natural world are (3)
direction and magnitude, force, velocity, acceleration
the position vector is the ———- going from the ——- to a particular ——. since the coordinates are all —-, the elements of a position vector is the same as the ——- of a ——
displacement vector, origin, point, zeroes, coordinates of a point
in order to find the direction vector, you take the second point and do an ———- from the first. the —— of the end point minus start isnt defined so you can get different forms
end point minus start point, order
vectors can be solved with the cosing equation when the two vectors are placed —- to —- or —- to —-
end to end, tail to tail
to numerically find the displacement vector between points, looking at the order of the letters you —— the ——- —— the ——
endpoint minus the start point
make sure that everything you write is ——-. always write it as an —-
equal to a vector, equation
vectors dont have a —— —-, and they can be —— or ——- without changing meaning
fixed position , translated or moved
vector geometry can only be done by addition of vectors. therefore, if given a subtraction number, you must ——- the ——— and put an ——- in front
flip the signs
the magnitude of a vector means a vectors —— therefore, magnitude can be calculated with ——
length, pythagorean theorum
in geometry to switch the negative form to positive you switch the —— —-
letter direction
in order to do dot product, you —— together corresponding points and then ——-. in the end of a dot product you should have ——-
multiply, add them up, 1 number
the dot product is not a vector its a —-
number
to determine if the vector is a unit vector, you take the values in the equation and plug it into. ———- form
pythagorean theorum
vectors are perpendicular when the angle between them is a ——-. numerically, they are perpendicular if their ——- equals ——
right angle, dot product is 0
numerically, vectors are parallel when they are —— —— of eachother
scaler multiples
a scaler is a number with —— but no ——. scalers are used to —— —-
scaler, magnitude, direction, multiply vectors
when you go against the direction of the vector in geometry it is —-
subtracted
pythagorian theorum for magnitude means taking all the — and then —— each value in ——. these numbers are then ———- to get length
values, squaring, parenthesis, square rooted
a vector is labelled using a ——- with an —— above it
variable, arrow
the dot product can be used to find the angle (-) between 2 vectors. this can only be done when the ——— are —— —— from eachother
vectors, pointing away from
1 unit long on x axis represented with ——, and 1 unit long on y axis represented with ——.
ī, j
