Vector Q1: Basic Results

The point \(A\), \(B\), \(C\) have position vectors \(\mathbf{a}\), \(\mathbf{b}\), \(\mathbf{c}\) respectively.

1. Given that \(2\mathbf{a}-3\mathbf{b}+\mathbf{c}=0\), show that \(A\), \(B\), \(C\) are collinear.[2]
2. Show that the point \(P\) with position vector \(\mathbf{p}\) given by \(\mathbf{p}=4\mathbf{a}-3\mathbf{b}\) lies on \(BA\) produced, and find the ratio \(BA:AP\).[3]