Lesson details
Key learning points
- Vectors can be added.
- This can be done when the vectors are in column form.
- Addition can be done when the vectors are drawn.
Keywords
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.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Two lines are parallel if they are straight lines that are always the (non-zero) distance apart.
Q2.Vectors with the same gradient are .
Q3.Match the pairs of parallel vectors.
$$4\choose8$$ -Â $$-2\choose-4$$
$$6\choose4$$ -Â $$12\choose8$$
$$-2\choose6$$ -Â $$1\choose-3$$
Q4.Which of the following vectors is not parallel to $$24\choose32$$?
Q5.The diagram shows a parallelogram. The base of the parallelogram is horizontal. What is the column vector for side $$a$$?
Q6.The diagram shows a parallelogram. The base of the parallelogram is horizontal. What is the column vector for side $$b$$?
Assessment exit quiz
6 Questions
Q1.A vector is the single vector that produces the same effect as a combination of other vectors.
Q2.Match each addition of two vectors to the correct resultant.
$$6\choose4$$ + $$-8\choose-7$$ -Â $$-2\choose-3$$
$$5\choose6$$ + $$-2\choose-8$$ -Â $$3\choose-2$$
$$4\choose-2$$ + $$-2\choose5$$ -Â $$2\choose3$$
$$3\choose-2$$ + $$0\choose4$$ -Â $$3\choose2$$
$$3\choose-2$$ + $$-5\choose5$$ -Â $$-2\choose3$$
$$6\choose6$$ + $$-9\choose-4$$ -Â $$-3\choose2$$
Q3.You are given that $${4\choose4} +{a\choose-7} = {12\choose-3}$$. The value of $$a$$ is .
Q4.You are given that $${-3\choose4}+ {a\choose2} + {-2\choose-1} = {-1\choose-5}$$. The value of $$a$$ is .
Q5.Which vector addition is represented by this diagram?
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.
