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      Multiplication with vectors

      Lesson details

      Learning outcome

      I can multiply with vectors.

      Key learning points

      1. Vectors can be multiplied by a scalar.
      2. Vectors cannot be multiplied by each other.
      3. Multiplication by a scalar can be done when the vectors are in column form.
      4. Multiplication by a scalar can be done when the vectors are drawn.

      Keywords

      • Scalar - A scalar is a quantity that has magnitude but not direction.

      • Displacement - Displacement is the distance from the starting point when measured in a straight line.

      Common misconception

      A reflection of a vector in the x or y axis is not the reverse of a vector. This is often seen with equilateral triangles and vectors.

      When multiplying the vectors by -1 this gives the opposite direction of the vector only. The magnitude remains the same. Investigate with pupils by drawing column vectors and multiply by -1 and compare.

      Teacher tip

      Pupils can create their own picture made of line segments and write down a set of instructions to create it.

      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.
      Find the additive inverse of $$ -4 \choose 3$$.

      $$ 4 \choose 3$$.
      $$ -3\choose 4$$.
      $$ 3\choose -4$$.
      Correct answer: $$ 4 \choose -3$$.

      Q2.
      Match each subtraction to its equivalent addition.

      Correct Answer:$${-3 \choose 2}-{1\choose 4}$$,$${-3 \choose 2}+{-1\choose -4}$$

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

      Correct Answer:$${-3 \choose 2}-{1\choose -4}$$,$${-3 \choose 2}+{-1\choose 4}$$

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

      Correct Answer:$${-3 \choose 2}-{-1\choose 4}$$,$${-3 \choose 2}+{1\choose -4}$$

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

      Correct Answer:$${-3 \choose 2}-{-1\choose -4}$$,$${-3 \choose 2}+{1\choose 4}$$

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

      Q3.
      Match each subtraction to its resultant.

      Correct Answer:$${-3 \choose 2}-{1\choose 4}$$,$${-4\choose -2}$$

      $${-4\choose -2}$$

      Correct Answer:$${-3 \choose 2}-{1\choose -4}$$,$${-4 \choose 6}$$

      $${-4 \choose 6}$$

      Correct Answer:$${-3 \choose 2}-{-1\choose 4}$$,$${-2 \choose -2}$$

      $${-2 \choose -2}$$

      Correct Answer:$${-3 \choose 2}-{-1\choose -4}$$,$${-2 \choose 6}$$

      $${-2 \choose 6}$$

      Q4.
      You are given that $${2\choose3}- {a\choose-3} = {-3\choose6}$$. The value of $$a$$ is .

      Correct Answer: 5

      Q5.
      Which vector subtraction can be represented by this diagram?

      An image in a quiz
      Correct answer: $${-5\choose3}-{-3\choose6}$$
      $${5\choose-3}-{3\choose-6}$$
      $${-6\choose3}-{-2\choose-3}$$
      $${3\choose-5}-{6\choose-3}$$
      $${-2\choose-3}-{-3\choose6}$$

      Q6.
      You are given that $${7\choose3}- {a\choose3} - {-3\choose-2} = {5\choose2}$$. The value of $$a$$ is .

      Correct Answer: 5

      6 Questions

      Q1.
      A is a quantity that has magnitude but not direction.

      Correct Answer: scalar

      Q2.
      The vector $$k {1 \choose 2}$$ represents the displacement A to B. The value of $$k$$ is .

      An image in a quiz
      Correct Answer: 4

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

      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
      An image in a quiz

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

      Correct Answer:$$3{8\choose6}$$,$$24\choose 18$$

      $$24\choose 18$$

      Correct Answer:$$-6{-4\choose3}$$,$$24\choose -18$$

      $$24\choose -18$$

      Correct Answer:$$2{-12\choose-9}$$,$$-24\choose -18$$

      $$-24\choose -18$$

      Correct Answer:$$-3{8\choose-6}$$,$$-24\choose 18$$

      $$-24\choose 18$$

      Q5.
      You are given that $$3 {5 \choose -4}= {a \choose b}$$ . Find the value of $$a$$ and of $$b$$.

      Correct answer: $$a=15$$
      $$a=8$$
      $$b=-4$$
      Correct answer: $$b=-12$$
      $$b=12$$

      Q6.
      You are given that $$x {6 \choose y}={24 \choose -36}$$. Find the value of $$x$$ and of $$y$$.

      $$x=-4$$
      Correct answer: $$x=4$$
      $$y=8$$
      $$y=9$$
      Correct answer: $$y=-9$$

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