So this is supposed to be a quite easy problem using an orthogonal base but I just can't figure it out :(. So Let $A,B,C \in \mathbb{R}^2 \text{ be three non-collinear, different from each other, points}$ Show every point $P\in \mathbb{R}^2$ can be represented with $p = \lambda a + \mu b + \nu c$ with $\lambda + \mu + \nu = 1$
The hint given by my professor was to think about orthogonal bases and orthogonal coordinate system but I just can't wrap my head around it... It would be amazing if you would have some ideas on how to approach this ^^