New
New
Year 11
Higher

Parallel vectors

I can identify column vectors which are parallel.

New
New
Year 11
Higher

Parallel vectors

I can identify column vectors which are parallel.

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Lesson details

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.

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.
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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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

Top left

Correct Answer:$$-5\choose-9$$,Top right

Top right

Correct Answer:$$-5\choose9$$,Bottom right

Bottom right

Correct Answer:$$5\choose9$$,Bottom left

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:$$4\choose12$$,$$6\choose18$$

$$6\choose18$$

Correct Answer:$$-2\choose12$$,$$-1\choose6$$

$$-1\choose6$$

Correct Answer:$$-5\choose-3$$,$$15\choose9$$

$$15\choose9$$

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: $$9\choose0$$
$$0\choose-9$$