Vector addition follows the triangle law (head-to-tail) or the parallelogram law (common tail). In component form: a + b = (a_{1}+b_{1})i + (a_{2}+b_{2})j + (a_{3}+b_{3})k. Addition is commutative (a + b = b + a) and associative. Scalar multiplication: ka = ka_{1}i + ka_{2}j + ka_{3}k. If k > 0, direction is preserved; if k < 0, direction reverses. Key property: |ka| = |k| · |a|. Two vectors are collinear (parallel) if a = kb for some scalar k. The vector from point A to point B is AB = b - a (position vector of B minus position vector of A).