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Year 11
Higher

Algebraic vector notation

I can represent information graphically given algebraic vector notation.

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New
New
Year 11
Higher

Algebraic vector notation

I can represent information graphically given algebraic vector notation.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. A letter can be used to represent a vector.
  2. Each unique vector is assigned a unique letter.

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: using highlighters can help to visualise this pathway.

If possible take the class outside. Draw some vectors on the floor with chalk. Ask pupils to get from different points on the diagram to others. They should carefully walk backwards where appropriate.
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.
Which of the following statements is correct about a vector quantity?
A vector has direction only.
A vector has magnitude only.
Correct answer: A vector has magnitude and direction.
A vector has neither magnitude nor direction.
Q2.
Find the resultant vector of $$4 {2\choose -3}+3{-1 \choose 2}$$.
$${-5\choose -6}$$
Correct answer: $${5\choose -6}$$
$${5\choose 6}$$
$${-5\choose 6}$$
Q3.
Find the resultant vector of $$4 {2\choose -3}-3{-1 \choose 2}$$.
$${5\choose -18}$$
$${5\choose -6}$$
$${11\choose -6}$$
Correct answer: $${11\choose -18}$$
Q4.
You are given that $$5 {-1\choose 2}- a{-2 \choose 4} = {-1 \choose 2}$$ . The value of $$a$$ is .
Correct Answer: 2
Q5.
Which of these diagrams can be used to illustrate $${12\choose -8}-2 {4 \choose 1}$$?
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
Q6.
You are given that $$3 {-1\choose5}+k{2 \choose-3} = {1 \choose y}$$. The value of $$y$$ is .
Correct Answer: 9

Exit quiz

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6 Questions

Q1.
Match each statement to the correct notation.
Correct Answer:$$\overrightarrow{OB}$$ ,A vector starting from $$O$$ and ending at $$B$$

A vector starting from $$O$$ and ending at $$B$$

Correct Answer:$$OB$$,A line segment with points $$O$$ and $$B$$ at each end

A line segment with points $$O$$ and $$B$$ at each end

Correct Answer:$$\overrightarrow{BO}$$ ,A vector starting from $$B$$ and ending at $$O$$

A vector starting from $$B$$ and ending at $$O$$

Correct Answer:$$(0, b)$$ ,A point with an $$x$$-coordinate of 0 and a $$y$$-coordinate of $$b$$

A point with an $$x$$-coordinate of 0 and a $$y$$-coordinate of $$b$$

Correct Answer:$$(b,0)$$ ,A point with an $$x$$-coordinate of $$b$$ and a $$y$$-coordinate of 0

A point with an $$x$$-coordinate of $$b$$ and a $$y$$-coordinate of 0

Q2.
Andeep draws this vector. What is this vector in column form?
An image in a quiz
Correct answer: $${2\choose 3}$$
$$(2,3)$$
$$(3,2)$$
$${3\choose 2}$$
Q3.
Laura draws this vector. What is this vector in column form?
An image in a quiz
Correct answer: $${6 \choose -1}$$
$$(6,-1)$$
$$(-1,6)$$
$${1 \choose 6}$$
$${-1 \choose 6}$$
Q4.
Jun draws two vectors and their resultant vector. He writes the resultant as $${8 \choose x}$$. Work out the value of $$x$$.
An image in a quiz
1
Correct answer: 2
3
-2
-1
Q5.
Which of the following vector statements are correct?
Correct answer: $${10 \choose -2} + {4 \choose 9}={14 \choose 7}$$
Correct answer: $$4{5 \choose 6}={20 \choose 24}$$
$$2{2.5 \choose -3.5}={6 \choose -7}$$
$${-4\choose 10} - {9 \choose 9}={-11\choose 1}$$
Correct answer: $${4\choose 9} + {-2 \choose -4}={2 \choose 5}$$
Q6.
Which of the following vector pathways are correct?
An image in a quiz
Correct answer: $$\overrightarrow{AC}=\overrightarrow{AB}+\overrightarrow{BC} $$
Correct answer: $$\overrightarrow{FC}=-\overrightarrow{CF}$$
$$\overrightarrow{EC}=-\overrightarrow{ED}-\overrightarrow{DC} $$
Correct answer: $$\overrightarrow{BD}=-\overrightarrow{CB}+\overrightarrow{CD} $$
$$\overrightarrow{DF}=\overrightarrow{CD}+\overrightarrow{CF}$$