dot and cross product

i'm trying to get better at studying, here's my attempt

dot product property

a • b = |a| |b| cos θ, where is the angle θ between the vectors

cross product

axb = |a| |b| sin θ n^, where θ is the angle between the scalar A unit vector perpendicular to the plane containing A and B

what quantity does a dot product result in?

scalar

what quantity does a cross product result in?

vector

holds [a • b = b • a]

dot product commutativity

doesn’t hold [a x b = -(b x a)]

cross product commutativity

scalar value, no direction

dot product direction

perpendicular to the plane containing A and B

cross product direction

orthogonality

concept of being independent

2 vectors are this if they are perpendicular to each other

in a math context, two vectors are orthogonal if their dot product is zero, and more generally, any two functions or vectors are orthogonal if their “inner product” is zero

a system design property which guarantees that modifying the technical effect produced by a component of a system neither creates nor propagates side effects other components of the system

two vectors are orthogonal if their dot product is zero

dot product orthogonality

the _____ product of two non-zero vectors is orthogonal to both of them

cross product orthogonality