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Year 11
Higher

Fluency in arithmetic procedures with algebraic vector notation

I can carry out arithmetic procedures on vectors written algebraically.

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New
New
Year 11
Higher

Fluency in arithmetic procedures with algebraic vector notation

I can carry out arithmetic procedures on vectors written algebraically.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. Priority of operations still apply.
  2. Like terms can be collected.
  3. The vectors can be sketched and the resultant shown.

Keywords

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

Common misconception

When using operations with vectors, pupils do not use the priority of operations.

The priority of operations applies to vectors, even those expressed in component form. Use Desmos to demonstrate a resultant vector using multiplication and/or addition of vectors.

Using Desmos, pupils can produce an arbitrary vector for a and an arbitrary vector b, and use Desmos to duplicate/scale these algebraic vectors and then see the resultant algebraic vector. e.g 2a + 3b, e.g. 5a - 3b.
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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Starter quiz

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6 Questions

Q1.
A __________ vector is the single vector that produces the same effect as a combination of other vectors.
end
final
overall
Correct answer: resultant
Q2.
Which of these vectors can be represented as $${-2 \choose -2}$$ in column form?
An image in a quiz
a
Correct answer: b
c
d
e
Q3.
Which of these vectors can be represented as $${2\choose 3}$$ in column form?
An image in a quiz
$$\overrightarrow{AB}$$
$$\overrightarrow{BD}$$
Correct answer: $$\overrightarrow{BC}$$
$$\overrightarrow{EB}$$
Q4.
Which of the following is equivalent to the resultant vector $${16 \choose -13} $$?
$$2{5 \choose -2} + 3{2 \choose 4}$$
$$2{4 \choose -7} + 5{-2 \choose 4}$$
Correct answer: $$3{4 \choose -7} + 2{2 \choose 4}$$
$$2{5 \choose -5} + 3{2 \choose -2}$$
Q5.
You are given that $$\overrightarrow{OB}= \mathbf{a}$$ and $$\overrightarrow{OA}=\mathbf{b}$$. Which of the following is the vector $$\overrightarrow{AB}$$?
$$\mathbf{a}+\mathbf{b}$$
$$\mathbf{a}-\mathbf{b}$$
Correct answer: $$\mathbf{b}-\mathbf{a}$$
$$\mathbf{b}+\mathbf{a}$$
Q6.
Which vector can be written in the form $$3\mathbf{a} -\mathbf{b} + 3\mathbf{d}$$?
An image in a quiz
$$\overrightarrow{OA}$$
$$\overrightarrow{OD}$$
$$\overrightarrow{BD}$$
$$\overrightarrow{CE}$$
Correct answer: $$\overrightarrow{OC}$$

Exit quiz

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6 Questions

Q1.
Vector $$\overrightarrow{AB}$$ is equivalent to __________.
An image in a quiz
$$2\overrightarrow{IJ}$$
$$\frac{1}{2}\overrightarrow{NM}$$
Correct answer: $$\frac{1}{2}\overrightarrow{CD}$$
$$\frac{1}{2}\overrightarrow{GH}$$
Q2.
Vector $$\overrightarrow{OA} = 20\mathbf{a} + 18\mathbf{b}$$. $$Y$$ is the midpoint of $$\overrightarrow{OA}$$. Find the vector $$\overrightarrow{OY}$$ in terms of $$\mathbf{a}$$ and $$\mathbf{b}$$
Correct answer: $$\overrightarrow{OY} = 10\mathbf{a} + 9\mathbf{b}$$
$$\overrightarrow{OY} = 40\mathbf{a} + 36\mathbf{b}$$
$$\overrightarrow{OY} = 5\mathbf{a} + 9\mathbf{b}$$
$$\overrightarrow{OY} = 20\mathbf{a} + 9\mathbf{b}$$
Q3.
Vector $$\overrightarrow{OA} = 20\mathbf{a} + 18\mathbf{b}$$. $$A$$ is the midpoint of $$\overrightarrow{OB}$$. Find the vector $$\overrightarrow{OB}$$ in terms of $$\mathbf{a}$$ and $$\mathbf{b}$$
$$\overrightarrow{OB} = 10\mathbf{a} + 9\mathbf{b}$$
Correct answer: $$\overrightarrow{OB} = 40\mathbf{a} + 36\mathbf{b}$$
$$\overrightarrow{OB} = 5\mathbf{a} + 9\mathbf{b}$$
$$\overrightarrow{OB} = 20\mathbf{a} + 9\mathbf{b}$$
Q4.
$$X$$ is the midpoint of the vector $$\overrightarrow{BD}$$. Which of the following statements are true?
An image in a quiz
Correct answer: $$\frac{1}{2}\overrightarrow{BD}=\overrightarrow{BX}$$
$$2\overrightarrow{BD}=\overrightarrow{BX}$$
Correct answer: $$\frac{1}{2}\overrightarrow{BD}=0.5\bigg({2\choose3}+{6\choose-1}\bigg)$$
$$\frac{1}{2}\overrightarrow{BD}= 2\bigg({2 \choose 3}+{6 \choose -1}\bigg)$$
Q5.
$$X$$ is the midpoint of the vector $$\overrightarrow{PQ}$$. Which of the following is vector $$\overrightarrow{PX}$$?
An image in a quiz
$$\overrightarrow{PX}= 14\mathbf{a}-16\mathbf{b}$$
$$\overrightarrow{PX}= 7\mathbf{a}-8\mathbf{b}$$
$$\overrightarrow{PX}= 7\mathbf{a}+8\mathbf{b}$$
Correct answer: $$\overrightarrow{PX}= 3.5\mathbf{a}-4\mathbf{b}$$
Q6.
The point $$X$$ is the midpoint of the vector $$\overrightarrow{OB}$$. Identify $$\overrightarrow{OX}$$.
An image in a quiz
$$\overrightarrow{OX}= 1.5\mathbf{a}+0.5\mathbf{b}$$
$$\overrightarrow{OX}= 3\mathbf{a}-\mathbf{b}$$
Correct answer: $$\overrightarrow{OX}= 1.5\mathbf{a}-0.5\mathbf{b}$$
$$\overrightarrow{OX}= 2.5\mathbf{a}-\mathbf{b}$$
$$\overrightarrow{OX}= 2.5\mathbf{a}+\mathbf{b}$$