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Year 11
Higher

Multiplication with vectors

I can multiply with vectors.

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New
New
Year 11
Higher

Multiplication with vectors

I can multiply with vectors.

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Share activities with pupils
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Lesson details

Key learning points

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

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.

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.

Pupils can create their own picture made of line segments and write down a set of instructions to create it.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Find the additive inverse of $$ -4 \choose 3$$.
$$ 4 \choose 3$$.
$$ -3\choose 4$$.
$$ 3\choose -4$$.
Correct answer: $$ 4 \choose -3$$.
Q2.
Match each subtraction to its equivalent addition.
Correct Answer:$${-3 \choose 2}-{1\choose 4}$$,$${-3 \choose 2}+{-1\choose -4}$$

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

Correct Answer:$${-3 \choose 2}-{1\choose -4}$$,$${-3 \choose 2}+{-1\choose 4}$$

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

Correct Answer:$${-3 \choose 2}-{-1\choose 4}$$,$${-3 \choose 2}+{1\choose -4}$$

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

Correct Answer:$${-3 \choose 2}-{-1\choose -4}$$,$${-3 \choose 2}+{1\choose 4}$$

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

Q3.
Match each subtraction to its resultant.
Correct Answer:$${-3 \choose 2}-{1\choose 4}$$,$${-4\choose -2}$$

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

Correct Answer:$${-3 \choose 2}-{1\choose -4}$$,$${-4 \choose 6}$$

$${-4 \choose 6}$$

Correct Answer:$${-3 \choose 2}-{-1\choose 4}$$,$${-2 \choose -2}$$

$${-2 \choose -2}$$

Correct Answer:$${-3 \choose 2}-{-1\choose -4}$$,$${-2 \choose 6}$$

$${-2 \choose 6}$$

Q4.
You are given that $${2\choose3}- {a\choose-3} = {-3\choose6}$$. The value of $$a$$ is .
Correct Answer: 5
Q5.
Which vector subtraction can be represented by this diagram?
An image in a quiz
Correct answer: $${-5\choose3}-{-3\choose6}$$
$${5\choose-3}-{3\choose-6}$$
$${-6\choose3}-{-2\choose-3}$$
$${3\choose-5}-{6\choose-3}$$
$${-2\choose-3}-{-3\choose6}$$
Q6.
You are given that $${7\choose3}- {a\choose3} - {-3\choose-2} = {5\choose2}$$. The value of $$a$$ is .
Correct Answer: 5

Exit quiz

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6 Questions

Q1.
A is a quantity that has magnitude but not direction.
Correct Answer: scalar
Q2.
The vector $$k {1 \choose 2}$$ represents the displacement A to B. The value of $$k$$ is .
An image in a quiz
Correct Answer: 4
Q3.
The diagram shows the vector a. Which of the following shows −0.25a?
An image in a quiz
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
Q4.
Match each scalar and vector to the resultant vector.
Correct Answer:$$3{8\choose6}$$,$$24\choose 18$$

$$24\choose 18$$

Correct Answer:$$-6{-4\choose3}$$,$$24\choose -18$$

$$24\choose -18$$

Correct Answer:$$2{-12\choose-9}$$,$$-24\choose -18$$

$$-24\choose -18$$

Correct Answer:$$-3{8\choose-6}$$,$$-24\choose 18$$

$$-24\choose 18$$

Q5.
You are given that $$3 {5 \choose -4}= {a \choose b}$$ . Find the value of $$a$$ and of $$b$$.
Correct answer: $$a=15$$
$$a=8$$
$$b=-4$$
Correct answer: $$b=-12$$
$$b=12$$
Q6.
You are given that $$x {6 \choose y}={24 \choose -36}$$. Find the value of $$x$$ and of $$y$$.
$$x=-4$$
Correct answer: $$x=4$$
$$y=8$$
$$y=9$$
Correct answer: $$y=-9$$