Parallel Vectors - Applications of Scalar Multiplication

This is an idea that we will see fairly a bit over the next couple of sections.  Two vectors are parallel if they have similar direction or are in precisely opposite directions.  Now, remind once again the geometric interpretation of scalar multiplication.  While we performed scalar multiplication we produced new vectors which were parallel to the original vectors (and each other for that matter).

Thus, let's suppose that a^→ and b^→ are parallel vectors. If they are parallel after that there must be a number c so that,  

a^→ = c^→b

Thus, two vectors are parallel if one is a scalar multiple of another.