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.

Calculating the magnitude of a vector

Maths

In the prior unit, pupils described a translation using column vector notation. Pupils' understanding of vectors is further developed in this unit, with pupils exploring column vector notation and arithmetic procedures.

Vectors

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

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.

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.

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.

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

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

__________ 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.

Match each vector expression to its resultant vector.

A right-angled triangle has a base length of 4 cm and a perpendicular height of 3 cm. Select the length of the hypotenuse. 

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

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

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.

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