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.

Dividing vectors into ratios

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

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

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

$$\frac{1}{5}\overrightarrow{AB}=\overrightarrow{AX}$$

$$\frac{1}{4}\overrightarrow{AB}=\overrightarrow{AX}$$

$$\frac{1}{2}\overrightarrow{AB}=\overrightarrow{AX}$$

$$\frac{4}{5}\overrightarrow{AB}=\overrightarrow{AX}$$

$$\frac{2}{5}\overrightarrow{AB}=\overrightarrow{AX}$$

X is a point on a line AB. Match each vector statement to the correct ratio.

$$\frac{1}{6}\overrightarrow{OL}=\overrightarrow{OB}$$

$$\frac{1}{2}\overrightarrow{OL}=\overrightarrow{OB}$$

$$\frac{11}{12}\overrightarrow{OL}=\overrightarrow{OB}$$

$$\frac{1}{12}\overrightarrow{OL}=\overrightarrow{OB}$$

B is a point on the line OL. Match each ratio to the correct vector statement.

O, A and B are in a straight line. You are given that $$\overrightarrow{OA}=12\mathbf{a}+20\mathbf{b}$$ and OA : AB is in the ratio 2 : 3. Work out vector $$\overrightarrow{AB}$$.

You are given that O, A and B are in a straight line,  $$\overrightarrow{OA}=12\mathbf{a}+20\mathbf{b}$$ and OB : BA is in the ratio 2 : 3. Work out vector $$\overrightarrow{BA}$$.

XYZ is a triangle. $$\overrightarrow{XY}= 5\mathbf{a}-7.5\mathbf{b}$$ and N lies on $$\overrightarrow{XY}$$ such that $$\overrightarrow{XN}=3\mathbf{a}-4.5\mathbf{b}$$. Write the ratio of XN : NY.

In triangle OAB, $$\overrightarrow{OA}=18\mathbf{a}$$, $$\overrightarrow{OB}=12\mathbf{b}$$. P is on AB. AP:PB = 1:2. $$\overrightarrow{OP}=k(6\mathbf{a}+2\mathbf{b})$$. The value of $$k$$ is {{ }}.

Work out the resultant vector for $${10 \choose -2} + {4 \choose 9}$$.

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

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

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

A vector starting from $$X$$ and ending at $$Y$$

A line segment with points $$X$$ and $$Y$$ at each end

Match each notation to its correct meaning.

Match each vector to an equivalent vector statement.

$$\frac{1}{2}(10\mathbf{a}+4\mathbf{b})$$

$$\frac{1}{3}(12\mathbf{a}+6\mathbf{b})$$

$$\frac{1}{5}(10\mathbf{a}+15\mathbf{b})$$

$$\frac{1}{2}(10\mathbf{a}-4\mathbf{b})$$

$$\frac{3}{4}(20\mathbf{a}-16\mathbf{b})$$

Match each vector statement to an equivalent vector statement.

$$\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}$$

$$-\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}$$

$$\overrightarrow{AB}+\overrightarrow{BC}-\overrightarrow{CD}$$

Select the vector path for $$\overrightarrow{AD}$$.

$$\frac{1}{2}\overrightarrow{IH}=\overrightarrow{CD}$$

$$2\overrightarrow{CD}=\overrightarrow{IH}$$

$$-\overrightarrow{IH}=\overrightarrow{HG}$$

$$-\overrightarrow{AB}=\overrightarrow{FE}$$

$$\frac{1}{2}\overrightarrow{FE}=\overrightarrow{BC}$$

Dividing vectors into ratios

Lesson outcome