Problem solving with vectors | Maths | Quizalize & Oak National Academy

Starter quiz

Displacement is the ______ from the starting point when measured in a straight line.

'distance' ✓
Find the resultant vector of $3 {-2\choose 3}+4{1 \choose -2}$ .

${2\choose -1}$

${-2\choose -1}$

${2\choose 1}$

${-2\choose 1}$ ✓
Find the resultant vector of $3 {-2\choose 3}-4{1 \choose -2}$ .

${-2\choose 17}$

${-2\choose 1}$

${-10\choose 17}$ ✓

${-2\choose -1}$

${10\choose -17}$
You are given that $5 {-1\choose 2}- a{-2 \choose 4} = {3 \choose -6}$ . The value of $a$ is ______.

'4' ✓
Which of these diagrams can be used to illustrate $2{6\choose -4}+\frac{1}{2} {-16 \choose -4}$ ?
You are given that $2 {-1\choose5}+k{2 \choose-3} = {-6\choose y}$ . The value of $y$ is ______.

'16' ✓

A __________ vector is the single vector that produces the same effect as a combination of other vectors.

parallel

product

resultant ✓

sum

translation
$The diagram shows two regular hexagons. Which of these vectors is equal to <Math>\mathbf p</Math>?$

The diagram shows two regular hexagons. Which of these vectors is equal to $\mathbf p$ ?

$\overrightarrow{KL}$ ✓

$\overrightarrow{OJ}$

$\overrightarrow{DJ}$ ✓

$\overrightarrow{IH}$ ✓

$\overrightarrow{JI}$
$The diagram shows two regular hexagons. Which of these vectors is equal to <Math>2\mathbf q</Math>?$

The diagram shows two regular hexagons. Which of these vectors is equal to $2\mathbf q$ ?

$\overrightarrow{ED}$

$\overrightarrow{OE}$

$\overrightarrow{EO}$ ✓

$\overrightarrow{OC}$

$\overrightarrow{CO}$
$The diagram shows two regular hexagons. Find the vector <Math>\overrightarrow {DE}</Math>.$

The diagram shows two regular hexagons. Find the vector $\overrightarrow {DE}$ .

$2(\mathbf p - \mathbf q)$ ✓

$2(\mathbf p + \mathbf q)$

$2(\mathbf q - \mathbf p)$

$2\mathbf q - \mathbf p$

$2\mathbf p - \mathbf q$
Given $\mathbf a = {2 \choose 3}$ and $\mathbf b = {-1 \choose 2}$ , find $3\mathbf a + 2 \mathbf b$

$1 \choose 5$

$4 \choose 5$

$8 \choose 5$

$4 \choose13$ ✓

$8 \choose13$
$a {3\choose -2} + 4{ 2 \choose b} = {14\choose 0}$ . The value of $b$ is ______

'1' ✓

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When calculating the resultant vector, pupils can incorrectly sum vectors due to opposite directions or proportions of vectors.

Encourage pupils to write a clear vector pathway, sometimes using highlighters can help visualise this pathway.

Vector - A vector can be used to describe a translation.
Displacement - Displacement is the distance from the starting point when measured in a straight line.
Resultant vector - A resultant vector is the single vector that produces the same effect as a combination of other vectors.