The sum and difference with algebraic vector notation | Maths

Starter quiz

Match the correct statement with the correct notation.

$\overrightarrow{AB}$

⇔

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 $a$ ✓
Which of the following represents this vector?

${3\choose 2}$ ✓

${2\choose 3}$

${-3\choose -2}$

${2\choose -3}$
Which of the following represents this vector?

${3\choose 2}$

${2\choose 3}$

${-3\choose -2}$ ✓

${2\choose -3}$
Match the resultant vectors.

${8 \choose -2} + {4 \choose 9}$

⇔

${12 \choose 7}$ ✓

$3{5 \choose 6}$

⇔

${15 \choose 18}$ ✓

${4\choose 9} + {-2 \choose -4}$

⇔

${2 \choose 5}$ ✓

${-4\choose 10} - {9 \choose 9}$

⇔

${-13\choose 1}$ ✓

$2{2.5 \choose -3.5}$

⇔

${5 \choose -7}$ ✓
Which of the following vector pathways are correct?

$\overrightarrow{DF}=\overrightarrow{DC}+\overrightarrow{CF}$ ✓

$\overrightarrow{AC}=\overrightarrow{AB}-\overrightarrow{BC}$

$\overrightarrow{EC}=-\overrightarrow{DE}-\overrightarrow{CD}$ ✓

$\overrightarrow{DC}=-\overrightarrow{CD}$ ✓

$\overrightarrow{BD}=\overrightarrow{CB}+\overrightarrow{CD}$
Match each $x$ value to the correct vector statement.

$x = 5$

⇔

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

$x=-7$

⇔

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

$x=2$

⇔

$4{x \choose 8} = {8 \choose 16}$ ✓

$x=8$

⇔

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

Exit quiz

Match each vector to the correct column vector.

$\mathbf{a}$

⇔

${6 \choose 0}$ ✓

$\mathbf{b}$

⇔

${-2 \choose -2}$ ✓

$\mathbf{c}$

⇔

${4 \choose -2}$ ✓

$\mathbf{d}$

⇔

${-2 \choose -3}$ ✓

$\mathbf{e}$

⇔

${-8\choose -2}$ ✓

$\mathbf{f}$

⇔

${-6\choose 1}$ ✓
Match each vector to the correct column vector.

$\overrightarrow{AB}$

⇔

${2\choose 2}$ ✓

$\overrightarrow{BC}$

⇔

${2\choose 3}$ ✓

$\overrightarrow{BD}$

⇔

${8\choose 2}$ ✓

$\overrightarrow{EA}$

⇔

${-8\choose 0}$ ✓

$\overrightarrow{EB}$

⇔

${-4\choose 2}$ ✓
Match each combination of vectors to the correct resultant.

$3{4 \choose -7} + 2{2 \choose 4}$

⇔

${16 \choose -13}$ ✓

$2{4 \choose -7} + 5{-2 \choose 4}$

⇔

${-2 \choose 6}$ ✓

$4{2 \choose 5}$

⇔

${8 \choose 20}$ ✓

$3{4 \choose -2} + 3{-2 \choose 5}$

⇔

${6 \choose 9}$ ✓
$Given <Math>\mathbf{a}={1\choose 3}</Math> and <Math>\mathbf{b}={2\choose -3}</Math>, write the resultant vector in terms of <Math>\mathbf{a}</Math> and <Math>\mathbf{b}</Math>.$

Given $\mathbf{a}={1\choose 3}$ and $\mathbf{b}={2\choose -3}$ , write the resultant vector in terms of $\mathbf{a}$ and $\mathbf{b}$ .

'3a+2b' ✓
$Find the vector <Math>\overrightarrow{PQ}</Math> in terms of <Math>\mathbf{a}</Math> and <Math>\mathbf{b}</Math>.$

Find the vector $\overrightarrow{PQ}$ in terms of $\mathbf{a}$ and $\mathbf{b}$ .

$7\mathbf{a}+8\mathbf{b}$

$7\mathbf{a}-8\mathbf{b}$ ✓

$7\mathbf{a}+6\mathbf{b}$

$3\mathbf{a}-8\mathbf{b}$
Match each vector to the correct vector pathway.

$\overrightarrow{OC}$

⇔

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

$\overrightarrow{BD}$

⇔

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

$\overrightarrow{AC}$

⇔

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

$\overrightarrow{CE}$

⇔

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

Worksheet

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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.

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.

Keywords

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