New
New
Year 11
•
Higher
Parallel vectors in algebraic vector notation
I can identify vectors written algebraically which are parallel.
New
New
Year 11
•
Higher
Parallel vectors in algebraic vector notation
I can identify vectors written algebraically which are parallel.
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.
Lesson details
Key learning points
- Parallel vectors have the same gradient.
- In algebraic form, this may be seen when one vector is a multiple of another.
- Vectors with opposite signs are parallel but act in opposite directions.
Keywords
Parallel - Two lines are parallel if they are straight lines that are always the same (non-zero) distance apart.
Common misconception
Parallel vectors can only be in the same direction.
Two vectors are parallel if one can be written as a scalar multiple of the other. This scalar multiple can be negative therefore the direction can be opposite, but the gradients remain equivalent.
Give pupils the opportunity to use Desmos to draw certain types of quadrilaterals e.g. trapeziums, parallelograms and irregular quadrilaterals. From these drawing, pupils can compare column vectors and identify if there is a scalar relationship with the vector lengths.
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
Loading...
Starter quiz
Download starter quiz
6 Questions
Q1.
Identify which of these statements are true.
Correct answer: Parallel vectors have the same gradient.
Parallel vectors have the same gradient.
Parallel vectors must be in the same direction.
Correct answer: Parallel vectors can have different magnitudes.
Parallel vectors can have different magnitudes.
Correct answer: Parallel vectors may have opposite directions.
Parallel vectors may have opposite directions.
All parallel vectors have the same length.
Q2.
Which of the following vectors are parallel to $${3 \choose 5}$$ ?
$${1.5 \choose 4}$$
Correct answer: $${6 \choose 10}$$
$${6 \choose 10}$$
Correct answer: $${12 \choose 20}$$
$${12 \choose 20}$$
$${5 \choose7}$$
Correct answer: $${1.5\choose 2.5}$$
$${1.5\choose 2.5}$$
Q3.
Which of the following vectors is parallel to $$\overrightarrow{IA}$$?
$$\overrightarrow{ED}$$
$$\overrightarrow{BC}$$
$$\overrightarrow{AB}$$
Correct answer: $$\overrightarrow{HG}$$
$$\overrightarrow{HG}$$
Q4.
Here is a regular hexagon with two labelled vectors. The centre of the hexagon is O. Select the vectors which are parallel to $$\overrightarrow{OX}$$.
$$\overrightarrow{QW}$$
Correct answer: $$\overrightarrow{QR}$$
$$\overrightarrow{QR}$$
$$\overrightarrow{RZ}$$
Correct answer: $$\overrightarrow{WX}$$
$$\overrightarrow{WX}$$
Correct answer: $$\overrightarrow{XW}$$
$$\overrightarrow{XW}$$
Q5.
Which of the following vectors are parallel to $${2 \choose -3}$$?
$${-3 \choose 2}$$
Correct answer: $${-8 \choose 12}$$
$${-8 \choose 12}$$
Correct answer: $${1 \choose -1.5}$$
$${1 \choose -1.5}$$
$${6 \choose -18}$$
Correct answer: $${-6 \choose 9}$$
$${-6 \choose 9}$$
Q6.
Match each column vector to its gradient.
Correct Answer:$${8\choose 4}$$,Gradient = $$\frac{1}{2}$$
$${8\choose 4}$$ -
Gradient = $$\frac{1}{2}$$
Correct Answer:$${4 \choose 8}$$,Gradient = $$2$$
$${4 \choose 8}$$ -
Gradient = $$2$$
Correct Answer:$${-4 \choose 8}$$,Gradient = $$-2$$
$${-4 \choose 8}$$ -
Gradient = $$-2$$
Correct Answer:$${8 \choose -4}$$,Gradient = $$-\frac{1}{2}$$
$${8 \choose -4}$$ -
Gradient = $$-\frac{1}{2}$$
Exit quiz
Download exit quiz
6 Questions
Q1.
Select the correct statements for parallel vectors. Parallel vectors __________.
Correct answer: are scalar multiples of one another
are scalar multiples of one another
are not collinear
Correct answer: can be in opposite directions
can be in opposite directions
can only be positive
Correct answer: have the same gradient
have the same gradient
Q2.
Which of these vectors are parallel to $${4 \choose -3}$$?
Correct answer: $${-8 \choose 6}$$
$${-8 \choose 6}$$
$${5 \choose -2}$$
Correct answer: $${40 \choose -30}$$
$${40 \choose -30}$$
Correct answer: $${2\choose -1.5}$$
$${2\choose -1.5}$$
$${6 \choose -7}$$
Q3.
Which of these vectors are parallel to $$3\mathbf{a}+5\mathbf{b}$$?
Correct answer: $$6\mathbf{a}+10\mathbf{b}$$
$$6\mathbf{a}+10\mathbf{b}$$
$$4\mathbf{a}+6\mathbf{b}$$
Correct answer: $$12\mathbf{a}+20\mathbf{b}$$
$$12\mathbf{a}+20\mathbf{b}$$
$$6\mathbf{a}+11\mathbf{b}$$
Correct answer: $$30\mathbf{a}+50\mathbf{b}$$
$$30\mathbf{a}+50\mathbf{b}$$
Q4.
Match each vector to a vector that is parallel to it.
Correct Answer:$$2\mathbf{a}+3\mathbf{b}$$,$$-2\mathbf{a}-3\mathbf{b}$$
$$2\mathbf{a}+3\mathbf{b}$$ -
$$-2\mathbf{a}-3\mathbf{b}$$
Correct Answer:$$3\mathbf{a}+2\mathbf{b}$$,$$6\mathbf{a}+4\mathbf{b}$$
$$3\mathbf{a}+2\mathbf{b}$$ -
$$6\mathbf{a}+4\mathbf{b}$$
Correct Answer:$$-2\mathbf{a}+3\mathbf{b}$$,$$-8\mathbf{a}+12\mathbf{b}$$
$$-2\mathbf{a}+3\mathbf{b}$$ -
$$-8\mathbf{a}+12\mathbf{b}$$
Correct Answer:$$2\mathbf{a}-3\mathbf{b}$$,$$-4\mathbf{a}+6\mathbf{b}$$
$$2\mathbf{a}-3\mathbf{b}$$ -
$$-4\mathbf{a}+6\mathbf{b}$$
Q5.
OACB is a parallelogram. M is the midpoint of OA and N is the midpoint of OB. $$\overrightarrow{OM}=10\mathbf{a}$$ and $$\overrightarrow{ON}=10\mathbf{b}$$. Select the correct scalar multipliers.
Correct answer: $$\frac{1}{2}\overrightarrow{AB}=\overrightarrow{MN}$$
$$\frac{1}{2}\overrightarrow{AB}=\overrightarrow{MN}$$
Correct answer: $$2\overrightarrow{MN}=\overrightarrow{AB}$$
$$2\overrightarrow{MN}=\overrightarrow{AB}$$
$$\frac{1}{3}\overrightarrow{AB}=\overrightarrow{MN}$$
$$3\overrightarrow{MN}=\overrightarrow{AB}$$
Q6.
ABCD is a kite. AX:XB = 1:1, BY:YC = 1:1, DZ:ZC = 1:1 and AW:WD=1:1, $$\overrightarrow{AW}= 3\mathbf{a}$$, $$\overrightarrow{AX}=3\mathbf{b}$$ and $$\overrightarrow{DZ}=3\mathbf{c}$$.
Correct answer: $$\overrightarrow{XY} = \overrightarrow{WZ}$$
$$\overrightarrow{XY} = \overrightarrow{WZ}$$
$$\overrightarrow{YC} = \overrightarrow{ZD}$$
$$\overrightarrow{AX} = \overrightarrow{AW}$$
Correct answer: $$\overrightarrow{XW} = \overrightarrow{YZ}$$
$$\overrightarrow{XW} = \overrightarrow{YZ}$$