A vector can be used to describe a translation.

Displacement is the distance from the starting point when measured in a straight line.

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

The additive inverse of a number is a number that, when added to the original number, gives the sum of 0.

Subtraction with vectors

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

Find the additive inverse of $$ 5 \choose -2$$

Match each subtraction to its equivalent addition.

You are given that $${-5\choose3}- {a\choose-2} = {-7\choose5}$$. The value of $$a$$ is {{ }}.  

Which vector subtraction can be represented by this diagram?

You are given that $${6\choose4}- {a\choose1} - {-3\choose-2} = {9\choose5}$$. The value of $$a$$ is {{ }}.  

A resultant vector is the {{ }} vector that produces the same effect as a combination of other vectors.

Match each addition of two vectors to the correct resultant.

You are given that $${1\choose4} + {a\choose-7} =  {4\choose-3}$$. The value of $$a$$ is {{ }}.

You are given that $${-3\choose4} + {a\choose2} + {-2\choose-7} =  {-4\choose-1}$$. The value of $$a$$ is {{ }}.  

Which vector addition is represented by this diagram?

Vector c is $${-8 \choose -3 }+ {-4 \choose -6}={-8 \choose 4 }$$

Vector c is $${-8 \choose -3 }- {-4 \choose -6}={-4 \choose4 }$$

Vector c is $${-8 \choose -2 }+ {-4 \choose -6}={-12\choose -8 }$$

Vector c is $$-2\times$$ vector d, so c and d are parallel & ABCD is a trapezium

Vectors c and d are equal, so parallel, & ABCD is a trapezium

ABCD is a quadrilateral. The vector a is $$-8\choose -2$$, the vector b is $$-4 \choose -6$$ and the vector d is $$6 \choose 4$$. Select the correct steps to show that ABCD is a trapezium. 

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