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).