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.

Algebraic vector notation

Maths

Checking and securing understanding of translations

Column vectors

Parallel vectors

Addition with vectors

Subtraction with vectors

Multiplication with vectors

Fluency in arithmetic procedures with vectors

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

A vector starting from $$O$$ and ending at $$B$$

A line segment with points $$O$$ and $$B$$ at each end

A vector starting from $$B$$ and ending at $$O$$

A point with an $$x$$-coordinate of 0 and a $$y$$-coordinate of $$b$$

A point with an $$x$$-coordinate of $$b$$ and a $$y$$-coordinate of 0

Match each statement to the correct notation.

Andeep draws this vector. What is this vector in column form?

Laura draws this vector. What is this vector in column form?

Jun draws two vectors and their resultant vector. He writes the resultant as $${8 \choose x}$$. Work out the value of $$x$$.

$${10 \choose -2} + {4 \choose 9}={14 \choose 7}$$

$${-4\choose 10} - {9 \choose 9}={-11\choose 1}$$

$${4\choose 9} + {-2 \choose -4}={2 \choose 5}$$

Which of the following vector statements are correct?

$$\overrightarrow{AC}=\overrightarrow{AB}+\overrightarrow{BC} $$

$$\overrightarrow{FC}=-\overrightarrow{CF}$$

$$\overrightarrow{EC}=-\overrightarrow{ED}-\overrightarrow{DC} $$

$$\overrightarrow{BD}=-\overrightarrow{CB}+\overrightarrow{CD} $$

$$\overrightarrow{DF}=\overrightarrow{CD}+\overrightarrow{CF}$$

Which of the following vector pathways are correct?

A vector has neither magnitude nor direction.

Which of the following statements is correct about a vector quantity?

Find the resultant vector of $$4 {2\choose -3}+3{-1 \choose 2}$$.

Find the resultant vector of $$4 {2\choose -3}-3{-1 \choose 2}$$.

You are given that  $$5 {-1\choose 2}- a{-2 \choose 4} = {-1 \choose 2}$$ . The value of $$a$$ is {{}}.

Which of these diagrams can be used to illustrate $${12\choose -8}-2 {4 \choose 1}$$?

You are given that $$3 {-1\choose5}+k{2 \choose-3} = {1 \choose y}$$. The value of $$y$$ is {{}}.

Algebraic vector notation

Lesson outcome