Vectors

Question 1

What are vectors?

Answer 1

Vectors are quantities that have both magnitude (size) and direction.

Question 2

Give examples of vector quantities

Answer 2

-Velocity
-Displacement
-Acceleration

Question 3

Column vectors

Answer 3

Represented as vertical columns, such as (⁵₃) indicating movement of 5 units right and 3 units up.

Question 4

Bold notation

Answer 4

Used in textbooks and exams, represented by bold characters like a.

Question 5

Arrow notation

Answer 5

Represented as → with AB underneath showing a vector going from point A to point B.

Question 6

Underlined (a type of vector notation)

Answer 6

Represented as a letter underlined, such as a.

Question 7

What happens when vectors are multiplied by scalars (numbers) ?

Answer 7

The size of the vector changes, but its direction remains the same.

Question 8

What do positive scalars do?

Answer 8

Scale up the vector while keeping the direction the same.

Question 9

What do negative scalars do?

Answer 9

Reverse the direction of the scalar.

Question 10

Be careful of…

Answer 10

…NEGATIVES

Question 11

What is a resultant vector?

Answer 11

A new vector made when two vectors are combined through addition or subtraction.

Question 12

What letter denotes a resulting vector?

Answer 12

R or this underlined if the a and b are

Question 13

How do we add vectors?

Answer 13

Align them tip to tail and the resulting vector runs from the tail of the first vector to the tip of the second.

Question 14

How do we subtract vectors?

Answer 14

Subtracting a vector is like adding its negative; it involves reversing the direction of the second vector before adding.

b = a - c in a triangle

Question 15

What does the magnitude of a vector tell us?

Answer 15

The size (length) of the vector.

Question 16

How do we find the length (magnitude/modulus) of a vector?

Answer 16

Use Pythagoras’ theorem

Question 17

How do we represent the length/magnitude/modulus of a vector?

Answer 17

I_I with an a in the middle

Question 18

How do we calculate the magnitude of the vector (⁵₃)

Answer 18

a = √1² + 5² = 5.10

Question 19

What is it worth doing when calculating the magnitude of a vector?

Answer 19

Drawing out the known sides as lengths in a triangle before trying to use Pythagoras’ theorem.

Question 20

How do we use vectors to find an unknown length?

Answer 20

Identify the route for the vector you want to find.

Substitute the known vectors.

Question 21

If an arrow goes from C to D but on your route you go from D to C, what does this mean?

Answer 21

you need a - CD

Question 22

What does the top number in a column vector mean?

Answer 22

How many squares to the right or left (if negative)?

Question 23

What does the bottom number in a column vector mean?

Answer 23

How many squares up or down (if negative)?

Question 24

What must we always do when writing a vector as a letter e.g. a in an exam?

Answer 24

UNDERLINE THE LETTER (because you can’t make it bold)

Question 25

Vectors that are scalar multiples of each other (e.g. 2a and -1.5a) are…

Answer 25

parallel

Question 26

what does a+b mean?

Answer 26

go along a and then b

Question 27

what does a-b mean?

Answer 27

go along a and then backwards along b