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

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

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 {{}}.

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