Resultant - A resultant vector is the single vector that produces the same effect as a combination of other vectors.
Vector - A vector can be used to describe a translation.
Displacement - Displacement is the distance from the starting point when measured in a straight line.

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; using highlighters can help to visualise this pathway.

Provide pupils with opportunities to carefully describe vector pathways. This could be done outside using chalk on the ground. This would give pupils the opportunity to physically walk the pathway.

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).

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Worksheet

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Starter quiz

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6 Questions

Q1.

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

Correct Answer: same

Q2.

Vectors with the same gradient are .

Correct Answer: parallel

Q3.

Match the pairs of parallel vectors.

Correct Answer:$$4\choose8$$,$$-2\choose-4$$

$$-2\choose-4$$

Correct Answer:$$6\choose4$$,$$12\choose8$$

$$12\choose8$$

Correct Answer:$$-2\choose6$$,$$1\choose-3$$

$$1\choose-3$$

Q4.

Which of the following vectors is not parallel to $$24\choose32$$?

$$3\choose4$$

$$-12\choose-16$$

$$48\choose64$$

Correct answer: $$6\choose4$$

Q5.

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

$$0\choose7$$

$$-1\choose3$$

$$-1\choose-3$$

Correct answer: $$1\choose3$$

$$0\choose-7$$

Q6.

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

$$0\choose7$$

Correct answer: $$7\choose0$$

$$0\choose-7$$

$$-7\choose0$$

Exit quiz

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6 Questions

Q1.

A vector is the single vector that produces the same effect as a combination of other vectors.

Correct Answer: resultant

Q2.

Match each addition of two vectors to the correct resultant.

Correct Answer:$$6\choose4$$ + $$-8\choose-7$$,$$-2\choose-3$$

$$-2\choose-3$$

Correct Answer:$$5\choose6$$ + $$-2\choose-8$$,$$3\choose-2$$

$$3\choose-2$$

Correct Answer:$$4\choose-2$$ + $$-2\choose5$$,$$2\choose3$$

$$2\choose3$$

Correct Answer:$$3\choose-2$$ + $$0\choose4$$,$$3\choose2$$

$$3\choose2$$

Correct Answer:$$3\choose-2$$ + $$-5\choose5$$,$$-2\choose3$$

$$-2\choose3$$

Correct Answer:$$6\choose6$$ + $$-9\choose-4$$,$$-3\choose2$$

$$-3\choose2$$

Q3.

You are given that $${4\choose4} +{a\choose-7} = {12\choose-3}$$. The value of $$a$$ is .

Correct Answer: 8

Q4.

You are given that $${-3\choose4}+ {a\choose2} + {-2\choose-1} = {-1\choose-5}$$. The value of $$a$$ is .

Correct Answer: 4

Q5.

Which vector addition is represented by this diagram?

$${-1\choose5}+{-2\choose-5}$$

Correct answer: $${-2\choose-5}+{-3\choose6}$$

$${-1\choose-5}+{-3\choose6}$$

$${2\choose5}+{3\choose-6}$$

$${1\choose5}+{3\choose6}$$

Q6.

ABCD is a quadrilateral. The vector a is $$-4\choose -1$$, the vector b is $$-2 \choose -3$$ and the vector d is $$3 \choose 2$$. Select the correct steps to show that ABCD is a trapezium.

Vector c is $${-4 \choose -1 }+ {-2 \choose -3}={-4 \choose 2 }$$

Correct answer: Vector c is $${-4 \choose -1 }+ {-2 \choose -3}={-6 \choose -4 }$$

Vector c is $${-4 \choose -1 }- {-2 \choose -3}={-2 \choose2 }$$

Vectors c and d are equal, so parallel, & ABCD is a trapezium

Correct answer: Vector c is $$-2\times$$ vector d, so c and d are parallel & ABCD is a trapezium