- Year 11
Subtraction with vectors
I can find the difference between vectors.
Lesson details
Key learning points
- Vectors can be subtracted.
- This can be done when the vectors are in column form.
- Subtraction can be done when the vectors are drawn.
Keywords
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.
Resultant vector - A resultant vector is the single vector that produces the same effect as a combination of other vectors.
Additive inverse - The additive inverse of a number is a number that, when added to the original number, gives the sum of 0.
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.A resultant vector is the vector that produces the same effect as a combination of other vectors.
Q2.Match each addition of two vectors to the correct resultant.
$$-6\choose4$$ + $$2\choose1$$ -Â $$-4\choose5$$
$$4\choose3$$ + $$-9\choose-7$$ -Â $$-5\choose-4$$
$$-2\choose1$$ + $$-2\choose-6$$ -Â $$-4\choose-5$$
$$-3\choose4$$ + $$-2\choose0$$ -Â $$-5\choose4$$
$$-1\choose7$$ + $$5\choose-2$$ -Â $$4\choose5$$
$$-2\choose6$$ + $$7\choose-2$$ -Â $$5\choose4$$
Q3.You are given that $${1\choose4} + {a\choose-7} = {4\choose-3}$$. The value of $$a$$ is .
Q4.You are given that $${-3\choose4} + {a\choose2} + {-2\choose-7} = {-4\choose-1}$$. The value of $$a$$ is .
Q5.Which vector addition is represented by this diagram?
Q6.ABCD is a quadrilateral. The vector a is $$-8\choose -2$$, the vector b is $$-4 \choose -6$$ and the vector d is $$6 \choose 4$$. Select the correct steps to show that ABCD is a trapezium.
Assessment exit quiz
6 Questions
Q1.Find the additive inverse of $$ 5 \choose -2$$
Q2.Match each subtraction to its equivalent addition.
$${-2 \choose 3}-{4\choose 1}$$ -Â $${-2 \choose 3}+{-4\choose -1}$$
$${-2 \choose 3}-{4\choose -1}$$ -Â $${-2 \choose 3}+{-4\choose 1}$$
$${-2 \choose 3}-{-4\choose 1}$$ -Â $${-2 \choose 3}+{4\choose -1}$$
$${-2 \choose 3}-{-4\choose -1}$$ -Â $${-2 \choose 3}+{4\choose 1}$$
Q3.Match each subtraction to its resultant.
$${-2 \choose 3}-{4\choose 1}$$ -Â $${-6 \choose 2}$$
$${-2 \choose 3}-{4\choose -1}$$ -Â $${-6 \choose 4}$$
$${-2 \choose 3}-{-4\choose 1}$$ -Â $${2 \choose 2}$$
$${-2 \choose 3}-{-4\choose -1}$$ -Â $${2 \choose 4}$$
Q4.You are given that $${-5\choose3}- {a\choose-2} = {-7\choose5}$$. The value of $$a$$ is .
Q5.Which vector subtraction can be represented by this diagram?
Q6.You are given that $${6\choose4}- {a\choose1} - {-3\choose-2} = {9\choose5}$$. The value of $$a$$ is .
