Multiplication with vectors | Maths | Quizalize & Oak National Academy

Starter quiz

Find the additive inverse of $-4 \choose 3$ .

$4 \choose 3$ .

$-3\choose 4$ .

$3\choose -4$ .

$4 \choose -3$ . ✓
Match each subtraction to its equivalent addition.

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

⇔

${-3 \choose 2}+{-1\choose -4}$ ✓

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

⇔

${-3 \choose 2}+{-1\choose 4}$ ✓

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

⇔

${-3 \choose 2}+{1\choose -4}$ ✓

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

⇔

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

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

⇔

${-4\choose -2}$ ✓

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

⇔

${-4 \choose 6}$ ✓

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

⇔

${-2 \choose -2}$ ✓

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

⇔

${-2 \choose 6}$ ✓
You are given that ${2\choose3}- {a\choose-3} = {-3\choose6}$ . The value of $a$ is ______.

'5' ✓
Which vector subtraction can be represented by this diagram?

${-5\choose3}-{-3\choose6}$ ✓

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

${-6\choose3}-{-2\choose-3}$

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

${-2\choose-3}-{-3\choose6}$
You are given that ${7\choose3}- {a\choose3} - {-3\choose-2} = {5\choose2}$ . The value of $a$ is ______.

'5' ✓

Exit quiz

A ______ is a quantity that has magnitude but not direction.

'scalar' ✓
$The vector <Math>k {1 \choose 2}</Math> represents the displacement A to B. The value of <Math>k</Math> is <span class="blank">______</span>.$

The vector $k {1 \choose 2}$ represents the displacement A to B. The value of $k$ is ______.

'4' ✓
The diagram shows the vector a. Which of the following shows −0.25a?
Match each scalar and vector to the resultant vector.

$3{8\choose6}$

⇔

$24\choose 18$ ✓

$-6{-4\choose3}$

⇔

$24\choose -18$ ✓

$2{-12\choose-9}$

⇔

$-24\choose -18$ ✓

$-3{8\choose-6}$

⇔

$-24\choose 18$ ✓
You are given that $3 {5 \choose -4}= {a \choose b}$ . Find the value of $a$ and of $b$ .

$a=15$ ✓

$a=8$

$b=-4$

$b=-12$ ✓

$b=12$
You are given that $x {6 \choose y}={24 \choose -36}$ . Find the value of $x$ and of $y$ .

$x=-4$

$x=4$ ✓

$y=8$

$y=9$

$y=-9$ ✓

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Lesson Details

Key learning points

Vectors can be multiplied by a scalar.
Vectors cannot be multiplied by each other.
Multiplication by a scalar can be done when the vectors are in column form.
Multiplication by a scalar can be done when the vectors are drawn.

Common misconception

A reflection of a vector in the x or y axis is not the reverse of a vector. This is often seen with equilateral triangles and vectors.

When multiplying the vectors by -1 this gives the opposite direction of the vector only. The magnitude remains the same. Investigate with pupils by drawing column vectors and multiply by -1 and compare.

Keywords

Scalar - A scalar is a quantity that has magnitude but not direction.
Displacement - Displacement is the distance from the starting point when measured in a straight line.