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

Checking and securing understanding of translations

Column vectors

Parallel vectors

Addition with vectors

Multiplication with vectors

Fluency in arithmetic procedures with vectors

Algebraic vector notation

Parallel vectors in algebraic vector notation

The sum and difference with algebraic vector notation

Fluency in arithmetic procedures with algebraic vector notation

Calculating the magnitude of a vector

Dividing vectors into ratios

Geometric proofs with vectors

Advanced problem solving with vectors

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.

In this unit, pupil understanding of vectors is deepened 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. 

Subtraction with vectors

Lesson outcome