Components And Properties Of Vectors
Bayani Gaba-gaba
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.
Manufura
- Find components and resolved parts of a vector
- Find the magnitude of a vector
- Understand and use position vectors, including the vectors i and j
- Understand and use unit vectors
- Use vectors to establish simple properties of geometrical figures including collinearity, parallel lines and concurrency
- Find the position vector of a point dividing a line in a given ratio
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- What is the magnitude of the vector 5i - 12j? A) 7 B) 13 C) 17 D) 169 Answer: B
- 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
- 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
- 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
- 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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