3.10 Vectors: concepts and algebraIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 3.10 Vectors: concepts and algebra

1. Vectors $\mathbf{p}=\begin{pmatrix}2 \\ -1 \\ 2\end{pmatrix}$ and $\mathbf{q}=\begin{pmatrix}1 \\ 3 \\ -4\end{pmatrix}$.
   Find the vector of magnitude $12$ that has the same direction as $\mathbf{p}$.2 marks
2. Relative to an origin $O$, the points $A$ and $B$ have position vectors $\overrightarrow{OA}=\begin{pmatrix}1 \\ 4 \\ -2\end{pmatrix}$ and $\overrightarrow{OB}=\begin{pmatrix}3 \\ 7 \\ 4\end{pmatrix}$.
   Find the position vector of the midpoint $M$ of $[AB]$.2 marks
3. A drone starts at the origin $O$, which is at ground level. The unit vectors $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$ point east, north and vertically upwards, and distances are in metres. The drone flies at constant speed $12$ m s$^{-1}$ in the direction of the vector $\mathbf{i}+2\mathbf{j}+2\mathbf{k}$.
   Find the velocity vector of the drone.3 marks