Vectors in two dimensionsAQA A-Level Maths: Mind map

Exam questions on Vectors in two dimensions

1. The vectors $\mathbf a$ and $\mathbf b$ are given by $\mathbf a=\begin{pmatrix}3\\ -2\end{pmatrix}$ and $\mathbf b=\begin{pmatrix}-1\\ 4\end{pmatrix}$.
   Find the value of $p$ for which $\mathbf a+p\mathbf b$ is parallel to the vector $\mathbf i$.2 marks
2. $ABCD$ is a parallelogram with $\overrightarrow{AB}=\mathbf a$ and $\overrightarrow{AD}=\mathbf b$.
   The point $M$ is the midpoint of $DC$. Find $\overrightarrow{AM}$ in terms of $\mathbf a$ and $\mathbf b$.2 marks
3. $\mathbf u=2\mathbf i+5\mathbf j$, $\mathbf v=\lambda\mathbf i-4\mathbf j$ and $\mathbf w=\mathbf i-\mathbf j$, where $\lambda$ is a constant.
   Given that $\mathbf u$ and $\mathbf v$ are parallel, find the value of $\lambda$.3 marks