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New
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Year 11
Foundation

Problem solving with vectors

I can use my knowledge of vectors to solve problems.

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New
New
Year 11
Foundation

Problem solving with vectors

I can use my knowledge of vectors to solve problems.

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These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

These resources were created for remote use during the pandemic and are not designed for classroom teaching.

Lesson details

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.


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

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.
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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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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