# 12 - Vector

1. A vector, in computing, is generally a _________. typically storing numbers.

two dimensional stack

three dimensional array

one dimensional array

2. Vectors typically have ______ unlike lists and queues.

fixed sizes

sizes of no more than 8 bits

sizes of no more than 2 bits for efficiency

variable sizes

3. The vector data structure can be used to represent the mathematical vector used in linear algebra
` Vectors are often used in computing in computer graphics and simulating physical systems.`

TRUE

FALSE

4. The following shows how a simple vector could be represented as a _______________
`R = (X, Y ) `

A list

An arrow

A function

5. The following image demonstrates how a simple vector could be represented as _________________ A function

A list

An arrow

6. The following shows how you could represent a simple vector as a function.
`F  :   S ---> R`

TRUE

FALSE

7. Which of the following statements best describes what is happening in the following code:
```{0: Val1, 1: Val2, 2: Val3, 3: Val4...}
```

A vector is being used to represent a linked list

A vector is being used to represent a hash table's keys

A dictionary structure is being used to represent a vector

A list is being used to represent a vector

8. What is the following visualisation showing?
`Note: the visualisation also shows the effect that is had upon the vector` Two right angle triangles with components added together - shows how you can add two vectors together

This is showing how to create triangles and different shapes from vectors

The visualisation is depicting the multiplication of the sides of a vector

It is showing how to cut a vector in half - this is useful in game design

9. A scalar is a value by which you __________________

multiply a vector.

subtract one vector from another

increment the value of the adjacent vectors

10. A scalar represents the scale by which you want to increase or decrease the vector.

FALSE

TRUE

11. What is the following excerpt showing/demonstrating:
```Multiplying two vectors together to produce
another vector.

For example: A =
(3,5) and B= (7,2)
Therefore the new vector will be

>> 3 x 7 + 5 x 2 = 31. ```

The beta product of two vectors

The sum + 1 of two vectors

The dot product of two vectors

The result when one vector is scaled to the given size (e.g. 3,5)

12. Read the following excerpt on convex combination and decide which of the statements provided are true.
```Convex combination of vectors?

===============================

A method of multiplying vectors that would
then produce the resulting vector within the
convex hull - This is a spatial representation
of the  vector space between two vectors.

Mathematically speaking: to perform what is known
as a convex combination, you will be multiplying
one vector either by a scalar, or by another vector.

This could be represented as:

D = ?AB + ?AC

Which of the following statements are true?
============================================

1. A and A are the two vectors

2. ? and ? represent the real number that each
vector will be multiplied by

3. ? and ? must both be greater than or equal
to 0 and ? + ? must equal 1.

4. D will then fall within the vector space.

5. AB and AC are the two vectors

6. ? and ? represent the two vectors
```

The statements 2,4,6 are true - the rest are not

All of the statements are true

Only 1, 2 and 5 are true

The statements 2,3,4,5 are all true (1 and 6 are not)

13. A vector quantity has both direction and ________________

pixels (resolution depth)

colour (scalar depth)

magnitude (size).

quantity (no of elements inside it)

14. A negative vector has the same magnitude as well as the exact same direction

TRUE

FALSE

15. Vectors can be multiplied by a scalar which changes the size of the vector _________________

as well as the direction

but not the direction.

as well as both the shape and direction

as well as the colour and resolution