Geometric proofs with vectors
I can produce geometric proofs to prove that points are collinear or that vectors are parallel.
Geometric proofs with vectors
I can produce geometric proofs to prove that points are collinear or that vectors are parallel.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- Your knowledge of the properties of polygons can be applied to vector problems.
- A regular polygon has a relationship between sides that can be represented with vector notation.
- Your knowledge can be used to identify vectors and multiples of known vectors.
- Through manipulation, you can prove certain properties.
Keywords
Collinear - When three or more points lie on a single straight line, these points are said to be collinear.
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
AX : XB is 1 : 4 -
$$\frac{1}{5}\overrightarrow{AB}=\overrightarrow{AX}$$
AX : XB is 3 : 8 -
$$\frac{3}{11}\overrightarrow{AB}=\overrightarrow{AX}$$
AX : XB is 1 : 1 -
$$\frac{1}{2}\overrightarrow{AB}=\overrightarrow{AX}$$
AX : XB is 3 : 1 -
$$\frac{3}{4}\overrightarrow{AB}=\overrightarrow{AX}$$
$$x = 13$$ -
$${x \choose -2} + {12 \choose 7} = {25 \choose 5} $$
$$x=12$$ -
$${x\choose -7} + {-7 \choose -7} = {5 \choose -14} $$
$$x=4$$ -
$$x{2 \choose 8} = {8 \choose 32} $$
$$x=8$$ -
$$3{3\choose 4} + {3 \choose -4} = {12 \choose x} $$
Exit quiz
6 Questions
