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.
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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.
To help you plan your year 11 maths lesson on: Dividing vectors into ratios, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Dividing vectors into ratios, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
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The assessment exit quiz will test your pupils' understanding of the key learning points.
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Explore more key stage 4 maths lessons from the Vectors unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
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
$$AX:XB \; \text{is} \; 1:4$$ -
$$\frac{1}{5}\overrightarrow{AB}=\overrightarrow{AX}$$
$$AX:XB \; \text{is} \; 1:3$$ -
$$\frac{1}{4}\overrightarrow{AB}=\overrightarrow{AX}$$
$$AX:XB \; \text{is} \; 1:1$$ -
$$\frac{1}{2}\overrightarrow{AB}=\overrightarrow{AX}$$
$$AX:XB \; \text{is} \; 4 : 1$$ -
$$\frac{4}{5}\overrightarrow{AB}=\overrightarrow{AX}$$
$$AX:XB \; \text{is} \; 2 : 3$$ -
$$\frac{2}{5}\overrightarrow{AB}=\overrightarrow{AX}$$
$$OB : BL \; \text{is} \; 1 : 5$$ -
$$\frac{1}{6}\overrightarrow{OL}=\overrightarrow{OB}$$
$$OB : BL \; \text{is} \; 1 : 1$$ -
$$\frac{1}{2}\overrightarrow{OL}=\overrightarrow{OB}$$
$$OB : BL \; \text{is} \; 11 : 1$$ -
$$\frac{11}{12}\overrightarrow{OL}=\overrightarrow{OB}$$
$$OB : BL \; \text{is} \; 1 : 11$$ -
$$\frac{1}{12}\overrightarrow{OL}=\overrightarrow{OB}$$