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Problem solving with vectors

Lesson details

Learning outcome

I can use my knowledge of vectors to solve problems.

Key learning points

  1. Drawing a diagram can make things clearer.
  2. Adding to an existing diagram can make things clearer.
  3. It can be helpful to start with what you know or can deduce.

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.

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, sometimes using highlighters can help visualise this pathway.

Teacher tip

Give pupils the opportunity to calculate a resultant column vector using scalars and summing other vectors. From here, they replace two known values with x and y, thus creating a problem solving question they can give to another pupil to solve.

Licence

This content is © Oak National Academy Limited (2025), 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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Prior knowledge starter quiz

6 Questions

Q1.
Displacement is the from the starting point when measured in a straight line.

Correct Answer: distance

Q2.
Find the resultant vector of $$3 {-2\choose 3}+4{1 \choose -2}$$.

$${2\choose -1}$$
$${-2\choose -1}$$
$${2\choose 1}$$
Correct answer: $${-2\choose 1}$$

Q3.
Find the resultant vector of $$3 {-2\choose 3}-4{1 \choose -2}$$.

$${-2\choose 17}$$
$${-2\choose 1}$$
Correct answer: $${-10\choose 17}$$
$${-2\choose -1}$$
$${10\choose -17}$$

Q4.
You are given that $$5 {-1\choose 2}- a{-2 \choose 4} = {3 \choose -6}$$ . The value of $$a$$ is .

Correct Answer: 4

Q5.
Which of these diagrams can be used to illustrate $$2{6\choose -4}+\frac{1}{2} {-16 \choose -4}$$?

An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz

Q6.
You are given that $$2 {-1\choose5}+k{2 \choose-3} = {-6\choose y}$$. The value of $$y$$ is .

Correct Answer: 16

6 Questions

Q1.
A __________ vector is the single vector that produces the same effect as a combination of other vectors.

parallel
product
Correct answer: resultant
sum
translation

Q2.
The diagram shows two regular hexagons. Which of these vectors is equal to $$\mathbf p$$?

An image in a quiz
Correct answer: $$\overrightarrow{KL}$$
$$\overrightarrow{OJ}$$
Correct answer: $$\overrightarrow{DJ}$$
Correct answer: $$\overrightarrow{IH}$$
$$\overrightarrow{JI}$$

Q3.
The diagram shows two regular hexagons. Which of these vectors is equal to $$2\mathbf q$$?

An image in a quiz
$$\overrightarrow{ED}$$
$$\overrightarrow{OE}$$
Correct answer: $$\overrightarrow{EO}$$
$$\overrightarrow{OC}$$
$$\overrightarrow{CO}$$

Q4.
The diagram shows two regular hexagons. Find the vector $$\overrightarrow {DE}$$.

An image in a quiz
Correct answer: $$2(\mathbf p - \mathbf q)$$
$$2(\mathbf p + \mathbf q)$$
$$2(\mathbf q - \mathbf p)$$
$$2\mathbf q - \mathbf p$$
$$2\mathbf p - \mathbf q$$

Q5.
Given $$\mathbf a = {2 \choose 3}$$ and $$\mathbf b = {-1 \choose 2}$$, find $$3\mathbf a + 2 \mathbf b$$

$$1 \choose 5$$
$$4 \choose 5$$
$$8 \choose 5$$
Correct answer: $$4 \choose13$$
$$8 \choose13$$

Q6.
$$ a {3\choose -2} + 4{ 2 \choose b} = {14\choose 0}$$. The value of $$b$$ is

Correct Answer: 1

To help you plan your 11 maths lesson on: Problem solving with vectors, download all teaching resources for free and adapt to suit your pupils' needs...