b being parallel to a in the same direction is exactly the same as saying there's one and only one λ with b=λa.
Module goal. Define the three linear operations, addition, subtraction, and scalar multiplication, by drawing arrows, and learn the rules that govern them.
eastmath.com · 27.2 Adding, Subtracting, and Scaling Vectors · 27.2.5 The Collinear Vector Theorem