vector v = vector v divided by the magnitude of the vector
magnitude
square root with all the numbers square inside
orthogonal
if a dot b(vectors) = 0 or pi/2 and are perpendicular
scalar is a number while vector isn't
dot product
take the same position in two vectors and then add then do the same for the others and add them up
angle between two vectors
vector a * vector b = magnitude of vector a * magnitude of vector b * cosine
parallel
theta = 0, vector a * vector b = magnitude of a and b. Or a cross product of b(both r vectors) =0 or pi
anti parallel
theta equal 180, dot product of vector a and b = - or magnitude a and b
cross product
when normal * vector does not equal zero, it isn't on the plane
a line in a xy plane is determined when a point on the line and the direction of the line are given
another way to determine if lines are parallel
take the direction vector from lines 1 and 2 and check if they are the same or multiple
perpendicular lines
find the variables t and s or some other variables, plug them in to determine if they are the same on both sides of the equation. which means they intersect