Vectors
Gbogbo ọrọ náà
A delivery drone needs more than a distance to reach its target: it needs a direction too. Fly 4 km the wrong way and you are further from the parcel than when you started. Vectors are the tool mathematics uses to carry size and direction together, and they turn awkward geometry problems, where a diagram only gets you so far, into clean algebra.
This topic builds vector notation and column vectors from the ground up, covers addition, subtraction, scalar multiplication and magnitude, and finishes with the technique examiners favour most: using vectors to prove that lines are parallel, that points are collinear, and that several lines meet at a single point.
Ebumnobi
- Understand scalar and vector quantities in two dimensions
- Understand and use vector notation including column vectors
- Represent a vector by a directed line segment
- Understand and use parallel vectors, unit vectors and position vectors
- Find the sum and difference of two vectors
- Calculate the modulus (magnitude) of a vector
- Multiply a vector by a scalar
- Find the resultant of two or more vectors
- Apply vector methods to simple geometrical problems including collinearity, parallel lines and concurrency
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Nnyocha Ọmụmụ
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 these is a vector quantity? A) Mass B) Temperature C) Velocity D) Area Answer: C
- What is the magnitude of the vector (8, -6)? A) 2 B) 10 C) 14 D) 100 Answer: B
- If a = (5, -2) and b = (-3, 6), what is a - b? A) (2, 4) B) (8, -8) C) (-8, 8) D) (2, -4) Answer: B
- Multiplying a vector by -3 will: A) triple its magnitude and keep the same direction B) triple its magnitude and reverse its direction C) divide its magnitude by 3 and reverse its direction D) keep the magnitude the same and reverse its direction Answer: B
- P, Q and R have position vectors such that PQ = 2(PR). What can you conclude? A) P, Q and R are collinear B) PQ is perpendicular to PR C) Q is the midpoint of PR D) Nothing can be concluded Answer: A
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Vectors
View vectors geometrically.
"Algebra and Trigonometry: Vectors" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/10-8-vectors. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction
Ndị otu ndị ọzọ bipụtara ha n'okpuru ikike mepere emepe, anyị na-ekele ha dị ka ha si chọọ. Njikọ na-emepe saịtị ha.
Meecha Ajụjụ Ule Ọmarịcha
Ị chọrọ ime ajụjụ ule ọmarịcha gbasara Vectors? Budata ngwa Green Bridge CBT iji nweta ajụjụ ule ọmarịcha na nyocha zuru ezu gbasara isiokwu a.
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