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Year 11
Higher

Calculating the magnitude of a vector

I can calculate the magnitude of a vector using Pythagoras' theorem.

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New
New
Year 11
Higher

Calculating the magnitude of a vector

I can calculate the magnitude of a vector using Pythagoras' theorem.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. A vector's magnitude can be calculated.
  2. This is the same as calculating the length of a line.
  3. Pythagoras' theorem can be used.

Keywords

  • Pythagoras' theorem - Pythagoras’ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.

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.

Vectors are so commonly used, people do not think of the real life applications. Have a discussion with pupils if they have experienced vectors other than playing games? E.g GPS and navigation - Vectors are used to represent positions, directions, and distances in navigation systems and GPS devices.
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.
__________ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.
Euclid's
Euler's
Newton's
Correct answer: Pythagoras'
Q2.
Match each vector expression to its resultant vector.
Correct Answer:$${10 \choose -2} + {4\choose 9}$$,$${14 \choose 7}$$

$${14 \choose 7}$$

Correct Answer:$$4{5 \choose 6}$$,$${20 \choose 24}$$

$${20 \choose 24}$$

Correct Answer:$${4\choose 9} + {-2 \choose -4}$$,$${2 \choose 5}$$

$${2 \choose 5}$$

Correct Answer:$${-4\choose 10} - {9 \choose 9}$$,$${-13\choose 1}$$

$${-13\choose 1}$$

Correct Answer:$$2{2.5 \choose -3.5}$$,$${5 \choose -7}$$

$${5 \choose -7}$$

Q3.
A right-angled triangle has a base length of 4 cm and a perpendicular height of 3 cm. Select the length of the hypotenuse.
2.5 cm
4 cm
Correct answer: 5 cm
6 cm
8 cm
Q4.
A right-angled triangle has a base length of 24 cm and a hypotenuse of 26 cm. Select the perpendicular height of the triangle.
Correct answer: 10 cm
13 cm
18 cm
20 cm
45 cm
Q5.
A square has lengths 5 cm. The length of the diagonal of the square is cm correct to 3 significant figures.
Correct Answer: 7.07, 7.07 cm, 7.07cm
Q6.
An isosceles triangle has a base length of 12 cm and side lengths of 16 cm. The perpendicular height of the triangle is cm correct to the nearest millimetre.
Correct Answer: 14.8 , 14.8 cm, 14.8cm

Exit quiz

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6 Questions

Q1.
Which of the following is the correct working out to find the length, $$c$$, of the vector $${9\choose 3}$$?
$$9^2+c^2 = 3^2$$
$$9^2-3^2 = c^2$$
Correct answer: $$9^2+3^2 = c^2$$
$$3^2-c^2 = 9^2$$
Q2.
The vector $${9\choose 3}$$ is drawn on squared paper. Each square has a side length of 1 cm. The length of the vector is cm to 1 decimal place.
Correct Answer: 9.5, 9.5cm, 9.5 cm
Q3.
You are given that $$\mathbf{a}= {2 \choose -3}$$ and $$\mathbf{b}= {4 \choose 4}$$. The magnitude of the vector $$\mathbf{a}+\mathbf{b}$$ is units to 3 s.f.
Correct Answer: 6.08, 6.08 cm, 6.08cm
Q4.
You are given that $$\mathbf{a}= {2 \choose -3}$$ and $$\mathbf{b}= {4 \choose 4}$$. The magnitude of the vector $$\mathbf{2a}-\mathbf{b}$$ is units to 3 s.f.
Correct Answer: 10, 10 cm, 10cm
Q5.
You are given that $$\overrightarrow{OA}={36 \choose 42}$$ and $$\overrightarrow{OB}={52 \choose 54}$$. The length of vector $$\overrightarrow{AB}$$ is units.
Correct Answer: 20, 20 cm, 20cm
Q6.
You are given that $$\overrightarrow{OA}={2 \choose4}$$, $$\overrightarrow{OB}={8 \choose 4}$$ and $$\overrightarrow{OC}={8\choose 10}$$. What type of triangle is $$ABC$$?
Equilateral
Isosceles
Right-angled
Correct answer: Right-angled isosceles
Scalene