1. The problem statement, all variables and given/known data If a, b and c are coplanar vectors related by λa+μb+νc=0, where the constants are non-zero, show that the condition for the points with position vectors αa, βb and γc to be collinear is: λ/α + μ/β + ν/γ = 0 2. Relevant equations Dot product Cross product Tripple product Vector equation of a line 3. The attempt at a solution I am fairly new to vectors, so I don't really know where to begin. Firstly, we know that for co-planar vectors, the tripple product is zero: [a,b,c]=0 Then, for the points so be colinear, the "slope" unit vector between them must be equal. Thus if we assume that point βb is in the middle: (αa-γc)/|αa-γc| = (αa-βb)/|αa-βb| From here what I can do is to expand the expressions in terms of the vector components, but this doesn't really bring me anywhere. I guess there should be an elegant solution without having to use components of vectors. Any suggestions where to begin? Many thanks!