Unit 13.1 Worked Example 1

The position vectors of two points \(A\) and \(B\) are \(\left( 3\mathbf{i}-\mathbf{j}+4\mathbf{k} \right)\) and \(\left( 2\mathbf{i}+\mathbf{j}+2\mathbf{k} \right)\) respectively. Points \(A\), \(B\) and \(C\) are collinear. Given that point \(C\) is \(6\) units away from \(A\) , find the possible position vectors of \(C\).