Subtraction with vectors | Maths | Quizalize & Oak National Academy

Starter quiz

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

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

$-6\choose4$ + $2\choose1$

⇔

$-4\choose5$ ✓

$4\choose3$ + $-9\choose-7$

⇔

$-5\choose-4$ ✓

$-2\choose1$ + $-2\choose-6$

⇔

$-4\choose-5$ ✓

$-3\choose4$ + $-2\choose0$

⇔

$-5\choose4$ ✓

$-1\choose7$ + $5\choose-2$

⇔

$4\choose5$ ✓

$-2\choose6$ + $7\choose-2$

⇔

$5\choose4$ ✓
You are given that ${1\choose4} + {a\choose-7} = {4\choose-3}$ . The value of $a$ is ______.

'3' ✓
You are given that ${-3\choose4} + {a\choose2} + {-2\choose-7} = {-4\choose-1}$ . The value of $a$ is ______.

'1' ✓
Which vector addition is represented by this diagram?

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

${3\choose-5}+{-6\choose3}$

${-6\choose3}+{2\choose3}$

${-5\choose3}+{3\choose-6}$ ✓

${5\choose-3}+{-3\choose6}$
$ABCD is a quadrilateral. The vector a is <Math>-8\choose -2</Math>, the vector b is <Math>-4 \choose -6</Math> and the vector d is <Math>6 \choose 4</Math>. Select the correct steps to show that ABCD is a trapezium.$

ABCD is a quadrilateral. The vector a is $-8\choose -2$ , the vector b is $-4 \choose -6$ and the vector d is $6 \choose 4$ . Select the correct steps to show that ABCD is a trapezium.

Vector c is ${-8 \choose -3 }+ {-4 \choose -6}={-8 \choose 4 }$

Vector c is ${-8 \choose -3 }- {-4 \choose -6}={-4 \choose4 }$

Vector c is ${-8 \choose -2 }+ {-4 \choose -6}={-12\choose -8 }$ ✓

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

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

Exit quiz

Find the additive inverse of $5 \choose -2$

$5 \choose -2$

$-5 \choose 2$ ✓

$-2 \choose 5$

$2 \choose -5$
Match each subtraction to its equivalent addition.

${-2 \choose 3}-{4\choose 1}$

⇔

${-2 \choose 3}+{-4\choose -1}$ ✓

${-2 \choose 3}-{4\choose -1}$

⇔

${-2 \choose 3}+{-4\choose 1}$ ✓

${-2 \choose 3}-{-4\choose 1}$

⇔

${-2 \choose 3}+{4\choose -1}$ ✓

${-2 \choose 3}-{-4\choose -1}$

⇔

${-2 \choose 3}+{4\choose 1}$ ✓
Match each subtraction to its resultant.

${-2 \choose 3}-{4\choose 1}$

⇔

${-6 \choose 2}$ ✓

${-2 \choose 3}-{4\choose -1}$

⇔

${-6 \choose 4}$ ✓

${-2 \choose 3}-{-4\choose 1}$

⇔

${2 \choose 2}$ ✓

${-2 \choose 3}-{-4\choose -1}$

⇔

${2 \choose 4}$ ✓
You are given that ${-5\choose3}- {a\choose-2} = {-7\choose5}$ . The value of $a$ is ______.

'2' ✓
Which vector subtraction can be represented by this diagram?

${-1\choose5}-{2\choose5}$

${-1\choose-5}-{3\choose-6}$

${2\choose5}-{-3\choose6}$

${-2\choose-5}-{3\choose-6}$ ✓

${1\choose5}-{-3\choose-6}$
You are given that ${6\choose4}- {a\choose1} - {-3\choose-2} = {9\choose5}$ . The value of $a$ is ______.

'0' ✓

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Lesson Details

Key learning points

Vectors can be subtracted.
This can be done when the vectors are in column form.
Subtraction 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

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.
Additive inverse - The additive inverse of a number is a number that, when added to the original number, gives the sum of 0.