Mathematics Specification A - 4MA1 PearsonEdexcel

Vectors

Gbogbo ọrọ náà

Vectors let you describe movement and position using both size and direction. Unlike ordinary numbers (scalars), a vector carries two pieces of information at once, making it the natural language for displacements, forces and velocities.

This topic covers vector notation, column vectors, addition and subtraction, scalar multiplication, magnitude, resultant vectors, and the use of vectors to prove geometrical results such as parallelism and collinearity. All content is Higher tier.

Ebumnobi

[Higher] Understand that a vector has both magnitude and direction
[Higher] Understand and use vector notation including column vectors
[Higher] Multiply vectors by scalar quantities
[Higher] Add and subtract vectors
[Higher] Calculate the modulus (magnitude) of a vector
[Higher] Find the resultant of two or more vectors
[Higher] Apply vector methods for simple geometrical proofs

Akọmọ Ojú-ẹkọ

A scalar has size (magnitude) only: temperature, mass or speed are all scalars. A vector has both magnitude and direction: displacement, velocity and force are vectors. The distinction matters because two displacements of 5 km can lead to very different positions if they point in different directions.

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Ayẹwo Ẹkọ

Ekele diri gi maka imecha ihe karịrị na Vectors. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.

Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.

Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.

Which of the following is a vector quantity? A) Temperature B) Mass C) Speed D) Displacement Answer: D
What is the magnitude of the vector (3, 4)? A) 7 B) 12 C) 5 D) 25 Answer: C
If a = (2, -3) and b = (1, 5), what is a + b? A) (3, 2) B) (3, -2) C) (1, 8) D) (-1, 2) Answer: A
Multiplying a vector by -2 will: A) double its magnitude and keep the same direction B) halve its magnitude and reverse direction C) double its magnitude and reverse direction D) keep the same magnitude and reverse direction Answer: C
Two vectors are parallel if: A) they have the same magnitude B) one is a scalar multiple of the other C) they are perpendicular D) they start from the same point Answer: B