Math
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unit vector
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


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

skew lines
neither perpendicular or parallel