Vectors in two dimensionsEdexcel A-Level Maths: Mind map

Exam questions on Vectors in two dimensions

1. The vectors $\mathbf{a}$ and $\mathbf{b}$ are given by $\mathbf{a}=5\mathbf{i}-12\mathbf{j}$ and $\mathbf{b}=-\mathbf{i}+3\mathbf{j}$.
   Find the exact value of $|\mathbf{a}+2\mathbf{b}|$.2 marks
2. The vector $\mathbf{p}$ is given by $\mathbf{p}=-4\mathbf{i}+4\sqrt{3}\,\mathbf{j}$.
   Find the vector of magnitude $24$ in the same direction as $\mathbf{p}$, giving your answer in terms of $\mathbf{i}$ and $\mathbf{j}$.2 marks
3. The vectors $\mathbf{a}$ and $\mathbf{b}$ are given by $\mathbf{a}=2\mathbf{i}+3\mathbf{j}$ and $\mathbf{b}=(k+1)\mathbf{i}+(k-2)\mathbf{j}$, where $k$ is a constant.
   Given that $\mathbf{b}$ is parallel to $\mathbf{a}$, find the value of $k$.3 marks