New
New
Year 11
Higher

The sum and difference with algebraic vector notation

I can find the sum and difference with vectors written algebraically.

New
New
Year 11
Higher

The sum and difference with algebraic vector notation

I can find the sum and difference with vectors written algebraically.

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Lesson details

Key learning points

  1. Addition and subtraction with vectors follows the algebraic manipulation rules you know.
  2. Vectors that are like terms can be collected.
  3. The resultant vector can be drawn by sketching.

Keywords

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

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; sometimes using highlighters can help visualize this pathway.

Give pupils the opportunity to create their own vector golf course where they choose 4 vectors and each shot is a multiple of a vector. They can then play this vector golf game with their peers.
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.
Match the correct statement with the correct notation.
Correct Answer:$$\overrightarrow{AB}$$,A vector starting from $$A$$ and ending at $$B$$

A vector starting from $$A$$ and ending at $$B$$

Correct Answer:$$AB$$,A line segment with points $$A$$ and $$B$$ at each end

A line segment with points $$A$$ and $$B$$ at each end

Correct Answer:$$\overrightarrow{BA}$$,A vector starting from $$B$$ and ending at $$A$$

A vector starting from $$B$$ and ending at $$A$$

Correct Answer:$$(a,b)$$,A point with $$x$$-coordinate of $$a$$ and $$y$$-coordinate of $$b$$

A point with $$x$$-coordinate of $$a$$ and $$y$$-coordinate of $$b$$

Correct Answer:$$(b,a)$$,A point with $$x$$-coordinate of $$b$$ and $$y$$-coordinate of $$a$$

A point with $$x$$-coordinate of $$b$$ and $$y$$-coordinate of $$a$$

Q2.
Which of the following represents this vector?
An image in a quiz
Correct answer: $${3\choose 2}$$
$${2\choose 3}$$
$${-3\choose -2}$$
$${2\choose -3}$$
Q3.
Which of the following represents this vector?
An image in a quiz
$${3\choose 2}$$
$${2\choose 3}$$
Correct answer: $${-3\choose -2}$$
$${2\choose -3}$$
Q4.
Match the resultant vectors.
Correct Answer:$${8 \choose -2} + {4 \choose 9}$$,$${12 \choose 7}$$

$${12 \choose 7}$$

Correct Answer:$$3{5 \choose 6}$$,$${15 \choose 18}$$

$${15 \choose 18}$$

Correct Answer:$${4\choose 9} + {-2 \choose -4}$$,$${2 \choose 5}$$

$${2 \choose 5}$$

Correct Answer:$${-4\choose 10} - {9 \choose 9}$$,$${-13\choose 1}$$

$${-13\choose 1}$$

Correct Answer:$$2{2.5 \choose -3.5}$$,$${5 \choose -7}$$

$${5 \choose -7}$$

Q5.
Which of the following vector pathways are correct?
An image in a quiz
Correct answer: $$\overrightarrow{DF}=\overrightarrow{DC}+\overrightarrow{CF}$$
$$\overrightarrow{AC}=\overrightarrow{AB}-\overrightarrow{BC} $$
Correct answer: $$\overrightarrow{EC}=-\overrightarrow{DE}-\overrightarrow{CD} $$
Correct answer: $$\overrightarrow{DC}=-\overrightarrow{CD}$$
$$\overrightarrow{BD}=\overrightarrow{CB}+\overrightarrow{CD} $$
Q6.
Match each $$x$$ value to the correct vector statement.
Correct Answer:$$x = 5$$,$${13 \choose -2} + {12 \choose 7} = {25 \choose x} $$

$${13 \choose -2} + {12 \choose 7} = {25 \choose x} $$

Correct Answer:$$x=-7$$,$${12 \choose x} + {-7 \choose -7} = {5 \choose -14} $$

$${12 \choose x} + {-7 \choose -7} = {5 \choose -14} $$

Correct Answer:$$x=2$$,$$4{x \choose 8} = {8 \choose 16} $$

$$4{x \choose 8} = {8 \choose 16} $$

Correct Answer:$$x=8$$,$${3\choose 4} + {x \choose -4} = {11 \choose 0} $$

$${3\choose 4} + {x \choose -4} = {11 \choose 0} $$

6 Questions

Q1.
Match each vector to the correct column vector.
An image in a quiz
Correct Answer:$$\mathbf{a}$$,$${6 \choose 0}$$

$${6 \choose 0}$$

Correct Answer:$$\mathbf{b}$$,$${-2 \choose -2}$$

$${-2 \choose -2}$$

Correct Answer:$$\mathbf{c}$$,$${4 \choose -2}$$

$${4 \choose -2}$$

Correct Answer:$$\mathbf{d}$$,$${-2 \choose -3}$$

$${-2 \choose -3}$$

Correct Answer:$$\mathbf{e}$$,$${-8\choose -2}$$

$${-8\choose -2}$$

Correct Answer:$$\mathbf{f}$$,$${-6\choose 1}$$

$${-6\choose 1}$$

Q2.
Match each vector to the correct column vector.
An image in a quiz
Correct Answer:$$\overrightarrow{AB}$$,$${2\choose 2}$$

$${2\choose 2}$$

Correct Answer:$$\overrightarrow{BC}$$,$${2\choose 3}$$

$${2\choose 3}$$

Correct Answer:$$\overrightarrow{BD}$$,$${8\choose 2}$$

$${8\choose 2}$$

Correct Answer:$$\overrightarrow{EA}$$,$${-8\choose 0}$$

$${-8\choose 0}$$

Correct Answer:$$\overrightarrow{EB}$$,$${-4\choose 2}$$

$${-4\choose 2}$$

Q3.
Match each combination of vectors to the correct resultant.
Correct Answer:$$3{4 \choose -7} + 2{2 \choose 4}$$,$${16 \choose -13} $$

$${16 \choose -13} $$

Correct Answer:$$2{4 \choose -7} + 5{-2 \choose 4}$$,$${-2 \choose 6} $$

$${-2 \choose 6} $$

Correct Answer:$$4{2 \choose 5}$$,$${8 \choose 20} $$

$${8 \choose 20} $$

Correct Answer:$$3{4 \choose -2} + 3{-2 \choose 5} $$,$${6 \choose 9} $$

$${6 \choose 9} $$

Q4.
Given $$\mathbf{a}={1\choose 3}$$ and $$\mathbf{b}={2\choose -3}$$, write the resultant vector in terms of $$\mathbf{a}$$ and $$\mathbf{b}$$.
An image in a quiz
Correct Answer: 3a+2b, 2b+3a, 3a + 2b, 2b + 3a
Q5.
Find the vector $$\overrightarrow{PQ}$$ in terms of $$\mathbf{a}$$ and $$\mathbf{b}$$.
An image in a quiz
$$7\mathbf{a}+8\mathbf{b}$$
Correct answer: $$7\mathbf{a}-8\mathbf{b}$$
$$7\mathbf{a}+6\mathbf{b}$$
$$3\mathbf{a}-8\mathbf{b}$$
Q6.
Match each vector to the correct vector pathway.
An image in a quiz
Correct Answer:$$\overrightarrow{OC}$$,$$3\mathbf{a} -\mathbf{b} + 3\mathbf{d}$$

$$3\mathbf{a} -\mathbf{b} + 3\mathbf{d}$$

Correct Answer:$$\overrightarrow{BD}$$,$$\mathbf{a} -4\mathbf{b} + 3\mathbf{d}$$

$$\mathbf{a} -4\mathbf{b} + 3\mathbf{d}$$

Correct Answer:$$\overrightarrow{AC}$$,$$\mathbf{a} -3\mathbf{b} + 3\mathbf{d}$$

$$\mathbf{a} -3\mathbf{b} + 3\mathbf{d}$$

Correct Answer:$$\overrightarrow{CE}$$,$$-\mathbf{a}-4\mathbf{b} - 2\mathbf{d}$$

$$-\mathbf{a}-4\mathbf{b} - 2\mathbf{d}$$