1. The problem statement, all variables and given/known data If possible, refer to attached image rather than whats written below (as the image is easier to understand). Triangle ABC is equilateral and AD = BE = CF. Let u, v and w be unit vectors in the directions of AB, BC and CA respectively. Let AB = mu and AD = nu. i) Find BC, BE, CA and CF. ii) Find |AE| and |FB| in terms of m and n. I don't understand why I can't use the Pythagoras equation to find their magnitudes. I've done hundreds of questions similar to this and have found the magnitudes of more vectors than I can remember, and this is the first time I've ever come across a vector where the equation doesn't apply. 2. Relevant equations |vector| = |ai+bj+ck| = sqrt(a^2 + b^2 + c^2) 3. The attempt at a solution I've attached a photo of my working. Basically, AE=AB+BE=mu+nv, so |AE|=sqrt((mu)^2 +(nv)^2) I know this is the wrong answer and wrong method. The correct method is: |AE| = sqrt((mu + nv)^2) = sqrt(m^2 -mn + n^2), as |u|=|v|=1 But I don't understand why that's the correct method! My tutor tried explaining it to me, he said that u, v, w are unit vectors but aren't "orthogonal" (I have little knowledge of what that means, I tried looking it up but all I could understand is that it has something to do with the vectors being right angles to each other??) and thus I can't use the i-j-k definition of magnitude for these vectors. That's all he said and I still don't understand graphically/visually how that works. Could you please provide a picture of what vector I can use the pythagoras theorem on and what vector I can't use it on? I'm a visual learner. As I wait for your responses, I will draw an accurately scaled version of this problem on a large sheet of paper and try to manually figure out the magnitude and see why the pythagoras theorem doesn't work. By the way, I have very little math foundation, so please avoid using complex terminology.