1. The problem statement, all variables and given/known data (I roughly translate the problem statement from German) Given the vectors a = (1,-2,3) and b = (1,1,1), divide the vector a in two components a1 (parallel to b) and a2 (perpendicular to b). 2. Relevant equations In a previous question of the problem, I found that: a.b = 2 a x b = (-5, 2, 3) |a| = √(14) ≈ 3.74 |b| = √(3) ≈ 1.73 So far, our class has been mentioning vector addition, multiplication by a real number, components of a vector, scalar product, vector product, as well as diverse properties of the operations I just listed (commutativity, distributivity, associativity and homogeneity). 3. The attempt at a solution My problem here is that the angle between the vectors is not given in the problem. I found several ways to calculate it with the use of arccos, but since that was not yet mentioned in my class, I am reluctant to use it. What I know so far is that: (I'll call ∂ the angle between a and b) a1 = |a| cos ∂ a2 = |a| sin ∂ a1 x b = 0 (because a1 and b are parallel, their cross product is equal to 0) a2.b = 0 (because a2 and b are perpendicular, their scalar product is equal to 0) since a.b = |a|.|b|.cos ∂, I also find that cos ∂ = 2/√(14).√(3) ≈ 0.31 I also know that a = √(a1^2 + a2^2) since the angle between a1 and a2 is π/2 rad. What am I missing to solve this problem? I just started a program of physic after many years without maths, so I need to refresh a bit :) Thank you very much for your answers, I appreciate it. Julien.