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Basics of vectors for AQA GCSE Maths

Basics of vectors

This page covers the following topics:

1. Vector basics
2. Column vectors
3. Equal vectors

Vector is a quantity with both a magnitude and a direction. In textbooks, vectors are denoted by a BOLD letter such as v. As it is hard to write bold letters in pen or paper, written work often uses different notation such as v, v, arrow or AB(arrow). The order of letters and arrows in the last example is important - in this case it tells us that the vector is going from point A to point B.

Vector basics

Column notation (column vectors) and horizontal bracket notation (row vectors) can be used to express vectors. Horizontal bracket notation has no commas between the components, and should not be confused with coordinates.

Column vectors

Equal vectors are vectors which have the same magnitude and direction, regardless of where they are located. Say we have a vector r, then the negative vector โˆ’r has the same magnitude as r, but points in the opposite direction.

Equal vectors

1

What is the magnitude and the direction of the vector shown?

magnitude = 5, x direction

What is the magnitude and the direction of the vector shown?

2

Which of the following are ways in which you can denote a vector as?
1) a (bold)
2) a (underlined)
3) ๐‘Žย โƒ—
4. (๐ด๐ต)ย โƒ—

All of them are ways in which you can denote vectors.

Which of the following are ways in which you can denote a vector as? 
1) a (bold) 
2) a (underlined) 
3) ๐‘Žย โƒ— 
4. (๐ด๐ต)ย โƒ—

3

What is another correct way in which we can denote vector v?

(AB)ย โƒ—

What is another correct way in which we can denote vector v?

4

From the image shown, what label would you give the vector next to the question mark?

(CB)ย โƒ—

From the image shown, what label would you give the vector next to the question mark?

5

Consider the following diagram (of a parallelogram). Vector r is the vector from C to A. What is the vector from D to B?

Note that the vector from C to A and the vector from D to B travel in the same direction, and also cover the same distance. Therefore they are equal vectors, so vector r also travels from D to B; DB = r.

Consider the following diagram (of a parallelogram). Vector r is the vector from C to A. What is the vector from D to B?

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