3.10 Vectors: concepts and algebraIB Maths: Applications and Interpretation HL: Flashcards

What these 13 flashcards ask

What is the difference between a scalar and a vector?
What are \mathbf{i}, \mathbf{j} and \mathbf{k}?
Write 3\mathbf{i}-2\mathbf{j}+5\mathbf{k} as a column vector.
How do you add two vectors in component form?
When are two vectors parallel?
What does -\mathbf{v} mean?
Formula for |\mathbf{v}| in 3D?
How do you find the unit vector in the direction of \mathbf{v}?
A vector with magnitude m in the direction of \mathbf{v}?
Velocity with speed 7 in direction 3\mathbf{i}+4\mathbf{j}?
Write \overrightarrow{AB} using position vectors.
Position vector of the midpoint of [AB]?
What is the resultant of two or more vectors?

Exam questions on 3.10 Vectors: concepts and algebra

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).