The sum and difference with algebraic vector notation
I can find the sum and difference with vectors written algebraically.
The sum and difference with algebraic vector notation
I can find the sum and difference with vectors written algebraically.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- Addition and subtraction with vectors follows the algebraic manipulation rules you know.
- Vectors that are like terms can be collected.
- 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.
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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Starter quiz
6 Questions
$$\overrightarrow{AB}$$ -
A vector starting from $$A$$ and ending at $$B$$
$$AB$$ -
A line segment with points $$A$$ and $$B$$ at each end
$$\overrightarrow{BA}$$ -
A vector starting from $$B$$ and ending at $$A$$
$$(a,b)$$ -
A point with $$x$$-coordinate of $$a$$ and $$y$$-coordinate of $$b$$
$$(b,a)$$ -
A point with $$x$$-coordinate of $$b$$ and $$y$$-coordinate of $$a$$
$${8 \choose -2} + {4 \choose 9}$$ -
$${12 \choose 7}$$
$$3{5 \choose 6}$$ -
$${15 \choose 18}$$
$${4\choose 9} + {-2 \choose -4}$$ -
$${2 \choose 5}$$
$${-4\choose 10} - {9 \choose 9}$$ -
$${-13\choose 1}$$
$$2{2.5 \choose -3.5}$$ -
$${5 \choose -7}$$
$$x = 5$$ -
$${13 \choose -2} + {12 \choose 7} = {25 \choose x} $$
$$x=-7$$ -
$${12 \choose x} + {-7 \choose -7} = {5 \choose -14} $$
$$x=2$$ -
$$4{x \choose 8} = {8 \choose 16} $$
$$x=8$$ -
$${3\choose 4} + {x \choose -4} = {11 \choose 0} $$
Exit quiz
6 Questions
$$\mathbf{a}$$ -
$${6 \choose 0}$$
$$\mathbf{b}$$ -
$${-2 \choose -2}$$
$$\mathbf{c}$$ -
$${4 \choose -2}$$
$$\mathbf{d}$$ -
$${-2 \choose -3}$$
$$\mathbf{e}$$ -
$${-8\choose -2}$$
$$\mathbf{f}$$ -
$${-6\choose 1}$$
$$\overrightarrow{AB}$$ -
$${2\choose 2}$$
$$\overrightarrow{BC}$$ -
$${2\choose 3}$$
$$\overrightarrow{BD}$$ -
$${8\choose 2}$$
$$\overrightarrow{EA}$$ -
$${-8\choose 0}$$
$$\overrightarrow{EB}$$ -
$${-4\choose 2}$$
$$3{4 \choose -7} + 2{2 \choose 4}$$ -
$${16 \choose -13} $$
$$2{4 \choose -7} + 5{-2 \choose 4}$$ -
$${-2 \choose 6} $$
$$4{2 \choose 5}$$ -
$${8 \choose 20} $$
$$3{4 \choose -2} + 3{-2 \choose 5} $$ -
$${6 \choose 9} $$
$$\overrightarrow{OC}$$ -
$$3\mathbf{a} -\mathbf{b} + 3\mathbf{d}$$
$$\overrightarrow{BD}$$ -
$$\mathbf{a} -4\mathbf{b} + 3\mathbf{d}$$
$$\overrightarrow{AC}$$ -
$$\mathbf{a} -3\mathbf{b} + 3\mathbf{d}$$
$$\overrightarrow{CE}$$ -
$$-\mathbf{a}-4\mathbf{b} - 2\mathbf{d}$$