New
New
Year 11
Higher

Subtraction with vectors

I can find the difference between vectors.

New
New
Year 11
Higher

Subtraction with vectors

I can find the difference between vectors.

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Lesson details

Key learning points

  1. Vectors can be subtracted.
  2. This can be done when the vectors are in column form.
  3. 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.

Give pupils a resultant vector and ask them to show on MWBs different vector sums which give this resultant vector.
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 resultant vector is the vector that produces the same effect as a combination of other vectors.
Correct Answer: single
Q2.
Match each addition of two vectors to the correct resultant.
Correct Answer:$$-6\choose4$$ + $$2\choose1$$,$$-4\choose5$$

$$-4\choose5$$

Correct Answer:$$4\choose3$$ + $$-9\choose-7$$,$$-5\choose-4$$

$$-5\choose-4$$

Correct Answer:$$-2\choose1$$ + $$-2\choose-6$$,$$-4\choose-5$$

$$-4\choose-5$$

Correct Answer:$$-3\choose4$$ + $$-2\choose0$$,$$-5\choose4$$

$$-5\choose4$$

Correct Answer:$$-1\choose7$$ + $$5\choose-2$$,$$4\choose5$$

$$4\choose5$$

Correct Answer:$$-2\choose6$$ + $$7\choose-2$$,$$5\choose4$$

$$5\choose4$$

Q3.
You are given that $${1\choose4} + {a\choose-7} = {4\choose-3}$$. The value of $$a$$ is .
Correct Answer: 3
Q4.
You are given that $${-3\choose4} + {a\choose2} + {-2\choose-7} = {-4\choose-1}$$. The value of $$a$$ is .
Correct Answer: 1
Q5.
Which vector addition is represented by this diagram?
An image in a quiz
$${-2\choose-3}+{3\choose-6}$$
$${3\choose-5}+{-6\choose3}$$
$${-6\choose3}+{2\choose3}$$
Correct answer: $${-5\choose3}+{3\choose-6}$$
$${5\choose-3}+{-3\choose6}$$
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.
An image in a quiz
Vector c is $${-8 \choose -3 }+ {-4 \choose -6}={-8 \choose 4 }$$
Vector c is $${-8 \choose -3 }- {-4 \choose -6}={-4 \choose4 }$$
Correct answer: Vector c is $${-8 \choose -2 }+ {-4 \choose -6}={-12\choose -8 }$$
Correct answer: Vector c is $$-2\times$$ vector d, so c and d are parallel & ABCD is a trapezium
Vectors c and d are equal, so parallel, & ABCD is a trapezium

6 Questions

Q1.
Find the additive inverse of $$ 5 \choose -2$$
$$ 5 \choose -2$$
Correct answer: $$ -5 \choose 2$$
$$ -2 \choose 5$$
$$ 2 \choose -5$$
Q2.
Match each subtraction to its equivalent addition.
Correct Answer:$${-2 \choose 3}-{4\choose 1}$$,$${-2 \choose 3}+{-4\choose -1}$$

$${-2 \choose 3}+{-4\choose -1}$$

Correct Answer:$${-2 \choose 3}-{4\choose -1}$$,$${-2 \choose 3}+{-4\choose 1}$$

$${-2 \choose 3}+{-4\choose 1}$$

Correct Answer:$${-2 \choose 3}-{-4\choose 1}$$,$${-2 \choose 3}+{4\choose -1}$$

$${-2 \choose 3}+{4\choose -1}$$

Correct Answer:$${-2 \choose 3}-{-4\choose -1}$$,$${-2 \choose 3}+{4\choose 1}$$

$${-2 \choose 3}+{4\choose 1}$$

Q3.
Match each subtraction to its resultant.
Correct Answer:$${-2 \choose 3}-{4\choose 1}$$,$${-6 \choose 2}$$

$${-6 \choose 2}$$

Correct Answer:$${-2 \choose 3}-{4\choose -1}$$,$${-6 \choose 4}$$

$${-6 \choose 4}$$

Correct Answer:$${-2 \choose 3}-{-4\choose 1}$$,$${2 \choose 2}$$

$${2 \choose 2}$$

Correct Answer:$${-2 \choose 3}-{-4\choose -1}$$,$${2 \choose 4}$$

$${2 \choose 4}$$

Q4.
You are given that $${-5\choose3}- {a\choose-2} = {-7\choose5}$$. The value of $$a$$ is .
Correct Answer: 2
Q5.
Which vector subtraction can be represented by this diagram?
An image in a quiz
$${-1\choose5}-{2\choose5}$$
$${-1\choose-5}-{3\choose-6}$$
$${2\choose5}-{-3\choose6}$$
Correct answer: $${-2\choose-5}-{3\choose-6}$$
$${1\choose5}-{-3\choose-6}$$
Q6.
You are given that $${6\choose4}- {a\choose1} - {-3\choose-2} = {9\choose5}$$. The value of $$a$$ is .
Correct Answer: 0