Dividing vectors into ratios
I can solve geometric problems in 2D where vectors are divided in a given ratio.
Dividing vectors into ratios
I can solve geometric problems in 2D where vectors are divided in a given ratio.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- A vector can be divided into parts using a ratio.
- By converting the ratio to a fraction, you can express each part in terms of the original vector.
- This allows you to perform further manipulations.
Keywords
Vector - A vector can be used to describe a translation.
Displacement - Displacement is the distance from the starting point when measured in a straight line.
Resultant vector - A resultant vector is the single vector that produces the same effect as a combination of other vectors.
Common misconception
When calculating the resultant vector, pupils can incorrectly sum vectors due to opposite directions or proportions of vectors.
Encourage pupils to write a clear vector pathway, sometimes using highlighters can help visualise this pathway.
Licence
This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Lesson video
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Starter quiz
6 Questions
$$\overrightarrow{OX}$$ -
A vector starting from $$O$$ and ending at $$X$$
$$OX$$ -
A line segment with points $$O$$ and $$X$$ at each end
$$\overrightarrow{XO}$$ -
A vector starting from $$X$$ and ending at $$O$$
$$\overrightarrow{XY}$$ -
A vector starting from $$X$$ and ending at $$Y$$
$$XY$$ -
A line segment with points $$X$$ and $$Y$$ at each end
$${12 \choose -9}$$ -
$$3\times {4 \choose -3}$$
$${16 \choose -12}$$ -
$$4\times {4 \choose -3}$$
$${-18 \choose -6}$$ -
$$2\times {-9 \choose -3}$$
$${4\choose -20}$$ -
$$-2\times {-2 \choose 10}$$
$${-27\choose -27}$$ -
$$-3\times {9 \choose 9}$$
$$5\mathbf{a}+2\mathbf{b}$$ -
$$\frac{1}{2}(10\mathbf{a}+4\mathbf{b})$$
$$4\mathbf{a}+2\mathbf{b}$$ -
$$\frac{1}{3}(12\mathbf{a}+6\mathbf{b})$$
$$2\mathbf{a}+3\mathbf{b}$$ -
$$\frac{1}{5}(10\mathbf{a}+15\mathbf{b})$$
$$5\mathbf{a}-2\mathbf{b}$$ -
$$\frac{1}{2}(10\mathbf{a}-4\mathbf{b})$$
$$15\mathbf{a}-12\mathbf{b}$$ -
$$\frac{3}{4}(20\mathbf{a}-16\mathbf{b})$$
Exit quiz
6 Questions
$$AX:XB \; \text{is} \; 1:4$$ -
$$\frac{1}{5}\overrightarrow{AB}=\overrightarrow{AX}$$
$$AX:XB \; \text{is} \; 1:3$$ -
$$\frac{1}{4}\overrightarrow{AB}=\overrightarrow{AX}$$
$$AX:XB \; \text{is} \; 1:1$$ -
$$\frac{1}{2}\overrightarrow{AB}=\overrightarrow{AX}$$
$$AX:XB \; \text{is} \; 4 : 1$$ -
$$\frac{4}{5}\overrightarrow{AB}=\overrightarrow{AX}$$
$$AX:XB \; \text{is} \; 2 : 3$$ -
$$\frac{2}{5}\overrightarrow{AB}=\overrightarrow{AX}$$
$$OB : BL \; \text{is} \; 1 : 5$$ -
$$\frac{1}{6}\overrightarrow{OL}=\overrightarrow{OB}$$
$$OB : BL \; \text{is} \; 1 : 1$$ -
$$\frac{1}{2}\overrightarrow{OL}=\overrightarrow{OB}$$
$$OB : BL \; \text{is} \; 11 : 1$$ -
$$\frac{11}{12}\overrightarrow{OL}=\overrightarrow{OB}$$
$$OB : BL \; \text{is} \; 1 : 11$$ -
$$\frac{1}{12}\overrightarrow{OL}=\overrightarrow{OB}$$