Calculating the magnitude of a vector | Maths | Quizalize & Oak National Academy

Starter quiz

__________ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.

Euclid's

Euler's

Newton's

Pythagoras' ✓
Match each vector expression to its resultant vector.

${10 \choose -2} + {4\choose 9}$

⇔

${14 \choose 7}$ ✓

$4{5 \choose 6}$

⇔

${20 \choose 24}$ ✓

${4\choose 9} + {-2 \choose -4}$

⇔

${2 \choose 5}$ ✓

${-4\choose 10} - {9 \choose 9}$

⇔

${-13\choose 1}$ ✓

$2{2.5 \choose -3.5}$

⇔

${5 \choose -7}$ ✓
A right-angled triangle has a base length of 4 cm and a perpendicular height of 3 cm. Select the length of the hypotenuse.

2.5 cm

4 cm

5 cm ✓

6 cm

8 cm
A right-angled triangle has a base length of 24 cm and a hypotenuse of 26 cm. Select the perpendicular height of the triangle.

10 cm ✓

13 cm

18 cm

20 cm

45 cm
A square has lengths 5 cm. The length of the diagonal of the square is ______ cm correct to 3 significant figures.

'7.07' ✓
An isosceles triangle has a base length of 12 cm and side lengths of 16 cm. The perpendicular height of the triangle is ______ cm correct to the nearest millimetre.

'14.8 ' ✓

Which of the following is the correct working out to find the length, $c$ , of the vector ${9\choose 3}$ ?

$9^2+c^2 = 3^2$

$9^2-3^2 = c^2$

$9^2+3^2 = c^2$ ✓

$3^2-c^2 = 9^2$
The vector ${9\choose 3}$ is drawn on squared paper. Each square has a side length of 1 cm. The length of the vector is ______ cm to 1 decimal place.

'9.5' ✓
You are given that $\mathbf{a}= {2 \choose -3}$ and $\mathbf{b}= {4 \choose 4}$ . The magnitude of the vector $\mathbf{a}+\mathbf{b}$ is ______ units to 3 s.f.

'6.08' ✓
You are given that $\mathbf{a}= {2 \choose -3}$ and $\mathbf{b}= {4 \choose 4}$ . The magnitude of the vector $\mathbf{2a}-\mathbf{b}$ is ______ units to 3 s.f.

'10' ✓
You are given that $\overrightarrow{OA}={36 \choose 42}$ and $\overrightarrow{OB}={52 \choose 54}$ . The length of vector $\overrightarrow{AB}$ is ______ units.

'20' ✓
You are given that $\overrightarrow{OA}={2 \choose4}$ , $\overrightarrow{OB}={8 \choose 4}$ and $\overrightarrow{OC}={8\choose 10}$ . What type of triangle is $ABC$ ?

Equilateral

Isosceles

Right-angled

Right-angled isosceles ✓

Scalene

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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.

Pythagoras' theorem - Pythagoras’ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.