Parallel vectors | Maths | Quizalize & Oak National Academy

Starter quiz

A ______ is a straight line from the start to end point and covers the shortest distance.

'vector' ✓
A vector has magnitude (size) and ______.

'direction' ✓
Which is the correct graphical representation of this vector? $-4\choose-3$
$The diagram shows the column vector <Math>a\choose-1</Math> represents. The value of <Math>a</Math> is <span class="blank">______</span>.$

The diagram shows the column vector $a\choose-1$ represents. The value of $a$ is ______.

'3' ✓
$The diagram shows the column vector <Math>a\choose-2</Math>. The value of <Math>a</Math> is <span class="blank">______</span>.$

The diagram shows the column vector $a\choose-2$ . The value of $a$ is ______.

'6' ✓
Match each vector to its best starting point.

$5\choose-9$

⇔

Top left ✓

$-5\choose-9$

⇔

Top right ✓

$-5\choose9$

⇔

Bottom right ✓

$5\choose9$

⇔

Bottom left ✓

Exit quiz

Two lines are ______ if they are straight lines that are always the same (non-zero) distance apart.

'parallel' ✓
Vectors are parallel if they have the same ______.

'gradient' ✓
Match the pairs of parallel vectors.

$4\choose12$

⇔

$6\choose18$ ✓

$-2\choose12$

⇔

$-1\choose6$ ✓

$-5\choose-3$

⇔

$15\choose9$ ✓
Which of the following vectors is not parallel to $12\choose15$ ?

$24\choose30$

$4\choose5$

$6\choose8$ ✓

$-36\choose-45$
The diagram shows a parallelogram. The base of the parallelogram is horizontal. What is the column vector for side $a$ ?

$6\choose3$

$0\choose9$

$3\choose6$ ✓

$9\choose0$
The diagram shows a parallelogram. The base of the parallelogram is horizontal. What is the column vector for side $b$ ?

$-9\choose0$

$0\choose9$

$9\choose0$ ✓

$0\choose-9$

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Lesson Details

Key learning points

Vectors are parallel if the gradient of each vector is the same.
If drawn, you can see this visually.
Parallel vectors are multiples of each other.

Common misconception

Parallel vectors must 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.

Keywords

Parallel - Two lines are parallel if they are straight lines that are always the same (non-zero) distance apart.
Gradient - The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the y-direction with respect to the positive x-direction.
Displacement - Displacement is the distance from the starting point when measured in a straight line.