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      Calculating the magnitude of a vector

      Lesson details

      Learning outcome

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

      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.

      Teacher tip

      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.

      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.
      __________ 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

      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

      To help you plan your 11 maths lesson on: Calculating the magnitude of a vector, download all teaching resources for free and adapt to suit your pupils' needs...