vectors Flashcards
R^n
R - the set of all real numbers
n - a positive integer
Rn- the set of all ordered n-tuples of real numbers. AKA the set of all vectors possible.
n-tuples
an ordered list of n elements
vector
a list of numbers
zero vector
a vector with all components are zero
ex: [0,0,0] or [0,0,0,0,0] etc.
scalar
a real number that describes magnitude and not direction. Used to scale vectors using scalar multiplication
addition and subtraction of vectors
v+u= [v1+u1, v2+u2] etc.
v-u=[v1-u1, v2-u2]
must have same number of components in each vector
head-to-tail rule
when adding vectors draw each vector head-to-tail
the vector from the tail of the first vector to the tip of the last vector represents the addition of all the vectors being added
parallelogram rule
draw 2 vectors being added where the tail starts at the same point. Create a parallelogram shape so that vectors u and u’, and v and v’ are across from each other in a parallelogram shape. The line that connects the starting point to the new point across the parallelogram is the addition of the 2 vectors.
scalar multiplication
To multiply a vector by a scalar, multiply each component by the scalar.
negative vector
A reversal of direction of the same vector. Multiply each component by -1.
equal vectors
when each component the vectors is equal to each other
parallel vectors
if two vectors are scalar multiples of each other, they are parallel.
v=cu
commutativity (of +)
u + v = v + u
associativity
(u + v) + w = u + (v + w)
cd)u = c(du
distribuitivity
c(u + v) = cu + cv
and other side
