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Year 11
Higher

Advanced problem solving with vectors

I can use my knowledge of vectors to solve problems.

icon-background-square
New
New
Year 11
Higher

Advanced problem solving with vectors

I can use my knowledge of vectors to solve problems.

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These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

These resources were created for remote use during the pandemic and are not designed for classroom teaching.

Lesson details

Key learning points

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

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.

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.


To help you plan your year 11 maths lesson on: Advanced problem solving with vectors, download all teaching resources for free and adapt to suit your pupils' needs...

Give pupils the opportunity to calculate a resultant column vector using scalars and summing other vectors. They replace two known values with x and y, thus creating a problem solving question which they could give to a peer to solve. For a greater challenge, replace a third value with z.
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Licence

This content is © Oak National Academy Limited (2025), 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.
Three points that lie along the ___________ are said to be collinear.
same curve
same pair of parallel lines
Correct answer: same straight line
Q2.
Select the correct statements to show that $$AEDB$$ is a trapezium.
An image in a quiz
Correct answer: $$\overrightarrow{AE}=2\overrightarrow{BD}$$
$$\overrightarrow{EA}=2\overrightarrow{BD}$$
$$2\overrightarrow{AE}=\overrightarrow{BD}$$
Correct answer: $$\overrightarrow{AB}\neq k\overrightarrow{ED}$$
$$\overrightarrow{AB}=\overrightarrow{ED}$$
Q3.
Select the correct statements to show that $$ABEF$$ is a parallelogram.
An image in a quiz
$$\overrightarrow{AF}=\overrightarrow{EB}$$
Correct answer: $$\overrightarrow{AF}=\overrightarrow{BE}$$
$$\overrightarrow{FA}=\overrightarrow{BE}$$
Correct answer: $$\overrightarrow{AB}=\overrightarrow{FE}$$
$$\overrightarrow{AB}=\overrightarrow{EF}$$
Q4.
$$ABCD$$ is a kite. The midpoints of each side are shown. $$\overrightarrow{WX} = k(\mathbf a - \mathbf b)$$ where $$k=$$ .
An image in a quiz
Correct Answer: 2
Q5.
$$ABCD$$ is a kite. $$W,X,Y,Z$$ are midpoints of the lines they lie on. Find $$\overrightarrow{WZ}$$.
An image in a quiz
$$- \mathbf c - \mathbf b$$
$$-2 \mathbf c -2 \mathbf b$$
Correct answer: $$2\mathbf b + 2\mathbf c$$
$$\mathbf c + \mathbf b$$
Q6.
$$ABCD$$ is a kite. $$W,X,Y,Z$$ are midpoints of the lines they lie on. Find $$\overrightarrow{ZX}$$.
An image in a quiz
$$- \mathbf c - 2\mathbf b + \mathbf a$$
$$ \mathbf c + 2\mathbf b - \mathbf a$$
Correct answer: $$-2 \mathbf c -4 \mathbf b + 2\mathbf a$$
$$ 2\mathbf c + 4\mathbf b - 2\mathbf a$$

6 Questions

Q1.
A vector is the single vector that produces the same effect as a combination of other vectors.
Correct Answer: resultant
Q2.
Given $$\mathbf a = {2 \choose 3}$$ and $$\mathbf b = {-1 \choose 2}$$, find $$4\mathbf a - 2 \mathbf b$$
$$8 \choose8$$
$$8 \choose4$$
$$6 \choose4$$
Correct answer: $$10 \choose8$$
$$10 \choose6$$
Q3.
Given that $$ x\choose 8$$ is parallel to $$ 15 \choose 12$$, then $$x =$$
Correct Answer: 10
Q4.
$$ a {3\choose -2} + 4{ 3 \choose b} = {3\choose 14}$$. The value of $$b$$ is
Correct Answer: 2
Q5.
Given that $$a {2\choose 1} + b{ 4 \choose4}= {16 \choose 14}$$, find the value of $$a + b$$. $$a+b=$$ .
Correct Answer: 5
Q6.
$$\mathbf a = {2\choose -3}$$ 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 .
Correct Answer: 4