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Learning objective

1. Depict vectors using directed line segments. 2. Apply position vectors. 3. Utilize the addition and subtraction of multiple vectors to express specified vectors in relation to two coplanar vectors. 4. Employ vectors for reasoning and resolving geometric problems, such as demonstrating that vectors are parallel, proving that three points are collinear, and tackling vector problems that involve ratios and similarity.

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Cambridge IGCSE MathematicsExtended Transformations and vectorsSupplement content

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1. Depict vectors using directed line segments. 2. Apply position vectors. 3. Utilize the addition and subtraction of multiple vectors to express specified vectors in relation to two coplanar vectors. 4. Employ vectors for reasoning and resolving geometric problems, such as demonstrating that vectors are parallel, proving that three points are collinear, and tackling vector problems that involve ratios and similarity

  • This point belongs to Vector geometry, especially Vector geometry outcomes.
  • You need to be able to 1. Depict vectors using directed line segments. 2. Apply position vectors. 3. Utilize the addition and subtraction of multiple vectors to express specified vectors in relation to two coplanar vectors. 4. Employ vectors for reasoning and resolving geometric problems, such as demonstrating that vectors are parallel, proving that three points are collinear, and tackling vector problems that involve ratios and similarity.
  • The key ideas to know are Show, Explain, and Determine.
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ShowExplainDetermineCalculate

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Paper 2 structured question: Vector geometry

Paper 2Core or Extended Mathematics3 marks

Diagram Description

Triangle with position vectors

Points A and B have position vectors \( \vec{a} \) and \( \vec{b} \) respectively relative to the origin O. Point C lies on the line segment AB such that AC:CB = 2:1.

PointPosition Vector
A\( \vec{a} \)
B\( \vec{b} \)
C?
  1. a

    Calculate Find the position vector of point C in terms of \( \vec{a} \) and \( \vec{b} \).

    Aim for approximately 3 distinct marking points.

    [3]
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