What do \mathbf i and \mathbf j represent?

Unit vectors of length 1 along the x-axis and the y-axis.

Add \begin{pmatrix}3\\ -2\end{pmatrix} and \begin{pmatrix}-1\\ 4\end{pmatrix}.

\begin{pmatrix}2\\ 2\end{pmatrix}, adding component by component.

What is the triangle law?

\overrightarrow{AB}+\overrightarrow{BC}=\overrightarrow{AC}: place vectors head to tail.

Express \overrightarrow{BA} in terms of \overrightarrow{AB}.

\overrightarrow{BA}=-\overrightarrow{AB}

What does k\mathbf a do to \mathbf a when k<0?

Multiplies the length by |k| and reverses the direction.

When are two vectors parallel?

When one is a scalar multiple of the other, \mathbf v=k\mathbf u.

A vector parallel to \mathbf i has what property?

Its \mathbf j-component is zero.

Vectors in two dimensionsAQA A-Level Maths: Flashcards

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What is the difference between a vector and a scalar?

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What is the difference between a vector and a scalar?: A vector has magnitude and direction; a scalar has magnitude only.
What do $\mathbf i$ and $\mathbf j$ represent?: Unit vectors of length $1$ along the $x$ -axis and the $y$ -axis.
Add $\begin{pmatrix}3\\ -2\end{pmatrix}$ and $\begin{pmatrix}-1\\ 4\end{pmatrix}$ .: $\begin{pmatrix}2\\ 2\end{pmatrix}$ , adding component by component.
What is the triangle law?: $\overrightarrow{AB}+\overrightarrow{BC}=\overrightarrow{AC}$ : place vectors head to tail.
Express $\overrightarrow{BA}$ in terms of $\overrightarrow{AB}$ .: $\overrightarrow{BA}=-\overrightarrow{AB}$
What does $k\mathbf a$ do to $\mathbf a$ when $k<0$ ?: Multiplies the length by $|k|$ and reverses the direction.
When are two vectors parallel?: When one is a scalar multiple of the other, $\mathbf v=k\mathbf u$ .
A vector parallel to $\mathbf i$ has what property?: Its $\mathbf j$ -component is zero.
Parallelogram $ABCD$ with $\overrightarrow{AB}=\mathbf a$ , $\overrightarrow{AD}=\mathbf b$ : $\overrightarrow{AC}$ ?: $\mathbf a+\mathbf b$
Same parallelogram: $\overrightarrow{BD}$ ?: $\mathbf b-\mathbf a$
If $X$ is on $PR$ with $PX:XR=2:1$ , what is $\overrightarrow{PX}$ ?: $\frac23\overrightarrow{PR}$
If $x_1\mathbf i+y_1\mathbf j=x_2\mathbf i+y_2\mathbf j$ , what follows?: $x_1=x_2$ and $y_1=y_2$ .

Exam questions on Vectors in two dimensions

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
$ABCD$ 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
$\mathbf u=2\mathbf i+5\mathbf j$ , $\mathbf v=\lambda\mathbf i-4\mathbf j$ 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

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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).