Addition with vectors | Maths | Quizalize & Oak National Academy

Starter quiz

Two lines are parallel if they are straight lines that are always the ______ (non-zero) distance apart.

'same' ✓
Vectors with the same gradient are ______.

'parallel' ✓
Match the pairs of parallel vectors.

$4\choose8$

⇔

$-2\choose-4$ ✓

$6\choose4$

⇔

$12\choose8$ ✓

$-2\choose6$

⇔

$1\choose-3$ ✓
Which of the following vectors is not parallel to $24\choose32$ ?

$3\choose4$

$-12\choose-16$

$48\choose64$

$6\choose4$ ✓
The diagram shows a parallelogram. The base of the parallelogram is horizontal. What is the column vector for side $a$ ?

$0\choose7$

$-1\choose3$

$-1\choose-3$

$1\choose3$ ✓

$0\choose-7$
The diagram shows a parallelogram. The base of the parallelogram is horizontal. What is the column vector for side $b$ ?

$0\choose7$

$7\choose0$ ✓

$0\choose-7$

$-7\choose0$

Exit quiz

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

'resultant' ✓
Match each addition of two vectors to the correct resultant.

$6\choose4$ + $-8\choose-7$

⇔

$-2\choose-3$ ✓

$5\choose6$ + $-2\choose-8$

⇔

$3\choose-2$ ✓

$4\choose-2$ + $-2\choose5$

⇔

$2\choose3$ ✓

$3\choose-2$ + $0\choose4$

⇔

$3\choose2$ ✓

$3\choose-2$ + $-5\choose5$

⇔

$-2\choose3$ ✓

$6\choose6$ + $-9\choose-4$

⇔

$-3\choose2$ ✓
You are given that ${4\choose4} +{a\choose-7} = {12\choose-3}$ . The value of $a$ is ______.

'8' ✓
You are given that ${-3\choose4}+ {a\choose2} + {-2\choose-1} = {-1\choose-5}$ . The value of $a$ is ______.

'4' ✓
Which vector addition is represented by this diagram?

${-1\choose5}+{-2\choose-5}$

${-2\choose-5}+{-3\choose6}$ ✓

${-1\choose-5}+{-3\choose6}$

${2\choose5}+{3\choose-6}$

${1\choose5}+{3\choose6}$
$ABCD is a quadrilateral. The vector a is <Math>-4\choose -1</Math>, the vector b is <Math>-2 \choose -3</Math> and the vector d is <Math>3 \choose 2</Math>. Select the correct steps to show that ABCD is a trapezium.$

ABCD is a quadrilateral. The vector a is $-4\choose -1$ , the vector b is $-2 \choose -3$ and the vector d is $3 \choose 2$ . Select the correct steps to show that ABCD is a trapezium.

Vector c is ${-4 \choose -1 }+ {-2 \choose -3}={-4 \choose 2 }$

Vector c is ${-4 \choose -1 }+ {-2 \choose -3}={-6 \choose -4 }$ ✓

Vector c is ${-4 \choose -1 }- {-2 \choose -3}={-2 \choose2 }$

Vectors c and d are equal, so parallel, & ABCD is a trapezium

Vector c is $-2\times$ vector d, so c and d are parallel & ABCD is a trapezium ✓

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

Video

Lesson Details

Key learning points

Vectors can be added.
This can be done when the vectors are in column form.
Addition can be done when the vectors are drawn.

Common misconception

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; using highlighters can help to visualise this pathway.

Keywords

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