Advanced problem solving with vectors | Maths | Quizalize & Oak National Academy

Starter quiz

Three points that lie along the ___________ are said to be collinear.

same curve

same pair of parallel lines

same straight line ✓
Select the correct statements to show that $AEDB$ is a trapezium.

$\overrightarrow{AE}=2\overrightarrow{BD}$ ✓

$\overrightarrow{EA}=2\overrightarrow{BD}$

$2\overrightarrow{AE}=\overrightarrow{BD}$

$\overrightarrow{AB}\neq k\overrightarrow{ED}$ ✓

$\overrightarrow{AB}=\overrightarrow{ED}$
Select the correct statements to show that $ABEF$ is a parallelogram.

$\overrightarrow{AF}=\overrightarrow{EB}$

$\overrightarrow{AF}=\overrightarrow{BE}$ ✓

$\overrightarrow{FA}=\overrightarrow{BE}$

$\overrightarrow{AB}=\overrightarrow{FE}$ ✓

$\overrightarrow{AB}=\overrightarrow{EF}$
$<Math>ABCD</Math> is a kite. The midpoints of each side are shown. <Math>\overrightarrow{WX} = k(\mathbf a - \mathbf b)</Math> where <Math>k=</Math><span class="blank">______</span>.$

$ABCD$ is a kite. The midpoints of each side are shown. $\overrightarrow{WX} = k(\mathbf a - \mathbf b)$ where $k=$ ______.

'2' ✓
$<Math>ABCD</Math> is a kite. <Math>W,X,Y,Z</Math> are midpoints of the lines they lie on. Find <Math>\overrightarrow{WZ}</Math>.$

$ABCD$ is a kite. $W,X,Y,Z$ are midpoints of the lines they lie on. Find $\overrightarrow{WZ}$ .

$- \mathbf c - \mathbf b$

$-2 \mathbf c -2 \mathbf b$

$2\mathbf b + 2\mathbf c$ ✓

$\mathbf c + \mathbf b$
$<Math>ABCD</Math> is a kite. <Math>W,X,Y,Z</Math> are midpoints of the lines they lie on. Find <Math>\overrightarrow{ZX}</Math>.$

$ABCD$ is a kite. $W,X,Y,Z$ are midpoints of the lines they lie on. Find $\overrightarrow{ZX}$ .

$- \mathbf c - 2\mathbf b + \mathbf a$

$\mathbf c + 2\mathbf b - \mathbf a$

$-2 \mathbf c -4 \mathbf b + 2\mathbf a$ ✓

$2\mathbf c + 4\mathbf b - 2\mathbf a$

Exit quiz

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

'resultant' ✓
Given $\mathbf a = {2 \choose 3}$ and $\mathbf b = {-1 \choose 2}$ , find $4\mathbf a - 2 \mathbf b$

$8 \choose8$

$8 \choose4$

$6 \choose4$

$10 \choose8$ ✓

$10 \choose6$
Given that $x\choose 8$ is parallel to $15 \choose 12$ , then $x =$ ______

'10' ✓
$a {3\choose -2} + 4{ 3 \choose b} = {3\choose 14}$ . The value of $b$ is ______

'2' ✓
Given that $a {2\choose 1} + b{ 4 \choose4}= {16 \choose 14}$ , find the value of $a + b$ . $a+b=$ ______.

'5' ✓
$\mathbf a = {2\choose -3}$ and $\mathbf b = {-2 \choose y}$ . Given that $3 \mathbf a - 2 \mathbf b$ is parallel to $30 \choose -51$ , the value of $y$ is ______.

'4' ✓

Worksheet

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Video

Lesson Details

Key learning points

Drawing a diagram can make things clearer.
Adding to an existing diagram can make things clearer.
It can be helpful to start with what you know or can deduce.

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 visualise this pathway.

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.