basics
two lines are perpendicular if the gradient of one line is the negative reciprocal of the other (incomplete)
dot product
commutative property of the dot product
distributive property of the dot product
associative property of the dot product
the dot product of a vector with itself gives the square of it's magnitude
deriving the geometric definition from the component-wise definition
deriving the component-wise definition from the geometric definition
cross product
anticommutative property of the cross product
distributive property of the cross product
scalar triple product is unchanged under a circular shift of its three operands