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

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

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

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

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

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

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

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 $$\overrightarrow{AD}$$.

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

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

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

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

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

This lesson will be removed by end of Summer Term 2025.

Dividing vectors into ratios

Lesson outcome

This lesson will be removed by end of Summer Term 2025.