Further Pure Mathematics - 4PM1 PearsonEdexcel

Components And Properties Of Vectors

Muhtasari

Vectors give you a precise way to describe position, displacement and direction using just two numbers. Once you can write any point as a position vector and any movement as a displacement, geometry becomes calculation: proving that points are collinear, finding where a line is divided in a given ratio, and identifying parallel lines all reduce to straightforward algebra on components.

This topic builds your fluency with the vector toolkit that runs through the 4PM1 specification. You will work with column vectors and the unit vectors i and j, calculate magnitudes, construct unit vectors, and apply the section formula. Every technique appears regularly in the Edexcel exam, so confident handling here pays off across the whole paper.

Malengo

  1. Find components and resolved parts of a vector
  2. Find the magnitude of a vector
  3. Understand and use position vectors, including the vectors i and j
  4. Understand and use unit vectors
  5. Use vectors to establish simple properties of geometrical figures including collinearity, parallel lines and concurrency
  6. Find the position vector of a point dividing a line in a given ratio

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Maelezo ya Somo

Navigation satellites pinpoint your location with coordinates. Air-traffic controllers track aircraft with direction and distance. Both are doing vector mathematics. In this topic you will learn to express positions, displacements and directions as vectors, compute their magnitudes, and use the results to prove geometric properties without a single compass or protractor.

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  1. What is the magnitude of the vector 5i - 12j? A) 7 B) 13 C) 17 D) 169 Answer: B
  2. If a = 3i + 4j, what is the unit vector in the direction of a? A) 3i + 4j B) (3/5)i + (4/5)j C) (3/7)i + (4/7)j D) (1/5)i + (1/5)j Answer: B
  3. Points A and B have position vectors 2i + j and 6i + 9j. What is the displacement vector AB? A) 8i + 10j B) -4i - 8j C) 4i + 8j D) 4i - 8j Answer: C
  4. If P divides AB in the ratio 1:3 where a = (0, 0) and b = (8, 12), what is the position vector of P? A) (2, 3) B) (4, 6) C) (6, 9) D) (3, 4) Answer: A
  5. Which condition proves that vectors a and b are parallel? A) |a| = |b| B) a = kb for some scalar k C) a + b = 0 D) a and b have the same direction only Answer: B

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Vitabu Vinavyopendekezwa

Pearson Edexcel International GCSE (9-1) Further Pure Mathematics Student Book
Pearson Edexcel International GCSE (9-1) Further Pure Mathematics Student Book
Manukuu: First edition
Mchapishaji: Pearson Education
Mwaka: 2017
ISBN: 978-0-435-18831-7
Maelezo: Endorsed student book covering the full 4PM1 specification.

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