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      Lesson details

      Learning outcome

      I can identify column vectors which are parallel.

      Key learning points

      1. Vectors are parallel if the gradient of each vector is the same.
      2. If drawn, you can see this visually.
      3. Parallel vectors are multiples of each other.

      Keywords

      • Parallel - Two lines are parallel if they are straight lines that are always the same (non-zero) distance apart.

      • Gradient - The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the y-direction with respect to the positive x-direction.

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

      Common misconception

      Parallel vectors must be in the same direction.

      Two vectors are parallel if one can be written as a scalar multiple of the other. This scalar multiple can be negative therefore the direction can be opposite, but the gradients remain equivalent.

      Teacher tip

      Use MWB when talking about shapes with parallel sides. Ask the pupils to draw examples of shapes with parallel sides and identify the sides which are parallel and also the same length.

      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.
      A is a straight line from the start to end point and covers the shortest distance.

      Correct Answer: vector

      Q2.
      A vector has magnitude (size) and .

      Correct Answer: direction

      Q3.
      Which is the correct graphical representation of this vector? $$-4\choose-3$$

      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

      Q4.
      The diagram shows the column vector $$a\choose-1$$ represents. The value of $$a$$ is .

      An image in a quiz
      Correct Answer: 3

      Q5.
      The diagram shows the column vector $$a\choose-2$$. The value of $$a$$ is .

      An image in a quiz
      Correct Answer: 6

      Q6.
      Match each vector to its best starting point.

      An image in a quiz
      Correct Answer:$$5\choose-9$$,Top left
      Correct Answer:$$-5\choose-9$$,Top right
      Correct Answer:$$-5\choose9$$,Bottom right
      Correct Answer:$$5\choose9$$,Bottom left

      6 Questions

      Q1.
      Two lines are if they are straight lines that are always the same (non-zero) distance apart.

      Correct Answer: parallel

      Q2.
      Vectors are parallel if they have the same .

      Correct Answer: gradient

      Q3.
      Match the pairs of parallel vectors.

      Correct Answer:$$4\choose12$$,$$6\choose18$$
      Correct Answer:$$-2\choose12$$,$$-1\choose6$$
      Correct Answer:$$-5\choose-3$$,$$15\choose9$$

      Q4.
      Which of the following vectors is not parallel to $$12\choose15$$?

      $$24\choose30$$
      $$4\choose5$$
      Correct answer: $$6\choose8$$
      $$-36\choose-45$$

      Q5.
      The diagram shows a parallelogram. The base of the parallelogram is horizontal. What is the column vector for side $$a$$?

      An image in a quiz
      $$6\choose3$$
      $$0\choose9$$
      Correct answer: $$3\choose6$$
      $$9\choose0$$

      Q6.
      The diagram shows a parallelogram. The base of the parallelogram is horizontal. What is the column vector for side $$b$$?

      An image in a quiz
      $$-9\choose0$$
      $$0\choose9$$
      Correct answer: $$9\choose0$$
      $$0\choose-9$$

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