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Fluency in arithmetic procedures with vectors

Lesson details

Learning outcome

I can carry out arithmetic procedures on vectors and draw the resultant vector.

Key learning points

  1. More than one operation may be seen.
  2. Priority of operations still apply.
  3. Constructing all the vectors can help when checking the resultant is correct.

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 using operations with vectors, pupils do not use the priority of operations.

The priority of operations applies to all calculations.

Teacher tip

Make a word using the letters in question 1 of task A and come up with questions with this word as the answer.

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.
Which of the following statements about a scalar quantity is correct?

A scalar has direction only.
Correct answer: A scalar has magnitude only.
A scalar has magnitude and direction.
A scalar has neither magnitude nor direction.

Q2.
The vector $$k {2 \choose 4}$$ represents the displacement A to B. The value of $$k$$ is .

An image in a quiz
Correct Answer: 2

Q3.
The diagram shows the vector a. Which of the following shows −0.25a?

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
An image in a quiz

Q4.
Match each scalar and vector to the resultant vector.

Correct Answer:$$3{12\choose8}$$,$$36\choose 24$$

$$36\choose 24$$

Correct Answer:$$-6{-6\choose4}$$,$$36\choose -24$$

$$36\choose -24$$

Correct Answer:$$2{-18\choose-12}$$,$$-36\choose -24$$

$$-36\choose -24$$

Correct Answer:$$-3{12\choose-8}$$,$$-36\choose 24$$

$$-36\choose 24$$

Q5.
You are given that $$-3 {4 \choose -6}= {a \choose b}$$ . Find the value of $$a$$ and of $$b$$.

$$a=12$$
Correct answer: $$a=-12$$
$$b=-6$$
Correct answer: $$b=18$$
$$b=-18$$

Q6.
You are given that $$x {8 \choose y}={24 \choose -15}$$. Find the value of $$x$$ and of $$y$$.

$$x=-3$$
Correct answer: $$x=3$$
$$y=-15$$
Correct answer: $$y=-5$$
$$y=5$$

6 Questions

Q1.
The distance from the starting point when measured in a straight line is called the .

Correct Answer: displacement

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

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

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

Correct Answer: 3

Q5.
Which of these diagrams can be used to illustrate $$4{3\choose -2}+2 {-4 \choose -1}$$?

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

Q6.
You are given that $$2 {-1\choose5}+k{2 \choose-3} = {4 \choose y}$$. The value of $$y$$ is .

Correct Answer: 1

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