Vectors Basics Flashcards
Define vector
quantity that is determined by its magnitude and direction
what is the magnitude of a vector
its length
what is a scalar
a number
what is a zero vector
a vector whos magnitude is 0 and who’s direction is undefined
how do we show a vector is a vector when handwriting
underline (or arrow above)
how do we show a vectors magnitude in handwriting
with a line either side ||
two vectors are equal when
they have the same magnitude and direction
what is the negative of a vector
same magnitude but different direction
how do we show a negative vector in handwriting
minus sign before the vector
if you multiply a vector by a positive scalar does its direction change
no
if you multiply a vector by a negative scalar does its direction change
Yes, goes in opposite direction
if you multiply a vector by 0, does its direction change
no, it becomes 0
what is a displacement vector
the vector which goes from one point on a plane to another
What is the x component of a vector
the change in x
what is the y component of a vector
the change in y
how to show vector addition on paper
parallelogram
how to show vector addition on paper
triangle rule
will multiplying a vector by a scalar change its magnitude
yes
vectors with magnitude of 1 are called
unit vectors
what can i represent
x component
what can j represent
y component
show the vector p in component form
pi + pj, (pi, pj)
how are vectors in a 2D and 3D plane equal
when their corresponding components are equal
too add vectors what do we do
add their corresponding components
to find the negative of vectors what do we do
find the negatives of their corresponding components
to subtract vectors what do we do
subtracts their corresponding components
to multiply a vector by a scalar what do we do
multiply each component by the scalar
how do we find the magnitude of a vector
squaring each component, adding answers, get square root of this answer
proj_a X is said
projection of vector x onto vector a
proj_a X formula
(vectorx • vetcora / ||a||^2 )vectora
why is there no difference between a vector that lies on a plane and a vector that is parallel to the plaen
the location of vectors don’t matter only their magnitude and direction. So if two vectors have the same magnitude and direction but lie on different parts of the plane, they are still the same vector
