Regarding geometric proofs with vectors, how much information and what information are we required to show by VCAA standards?
So, would saying that the diagonals of a rectangle bisect each other and there is one pair of perpendicular vectors be sufficient for a rectangle? Could we do the same with squares?
And what about rhombuses and parrallelograms? What is the bare minimum of information we would need to show for these?
How often do vector proofs come up in exams?
And some more questions too:
-What are the applications of the geometric representation of the dot product, apart from being able to find the angle between 2 vectors and the magnitude of those vectors?
-If we can use vector projections (the vector resolute I mean) to decompose a vector into rectangular components, then how can we apply this to the i, j and k unit vectors, as these are also a form of vector projections? Does anyone have a link to a proof of this concept? I am not quite sure what to search for this topic.
-How is the formal definition of linear dependence derived? I understand the derivation of its practical definition but cannot seem to understand its formal defintion. Please help. :/
thanks.