What is the sum of the vectors (1, 2) and (3, 4)?

(4, 6). Add the tops and add the bottoms.

What is 2 × the vector (3, −1)?

(6, −2). Multiply both parts by 2.

A and B have position vectors a and b. What is the vector from A to B?

b − a. Go from A back to the origin (−a), then out to B (+b).

Vectors · Cambridge IGCSE Mathematics 0580 revision

In plain words

A vector is a journey: so far across and so far up. It has a size and a direction but no fixed starting place. Vectors can be added (one journey after another) and stretched (the same direction, further).

Three things to know

A column vector has the movement across on top and the movement up underneath. Add vectors by adding the tops and adding the bottoms. Multiply by a number by multiplying both parts.
The magnitude (length) of a vector with parts x and y is √(x² + y²).
Going from A to B is the same as going back to the origin and out again: AB = b − a. Two vectors are parallel if one is a multiple of the other.

Worked example

Find the magnitude of the vector with parts 3 across and 4 up.

The magnitude is the length of the diagonal: use Pythagoras.
√(3² + 4²) = √25.
= 5.

Tips and tricks

Going against the arrow reverses the sign: BA = −AB.
To get from one point to another in a diagram, follow any route along vectors you know and add them up.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Vectors: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

What is the sum of the vectors (1, 2) and (3, 4)?
- (4, 6) (the answer)
- (3, 8)
- (2, 2)
- (4, 8)
Add the tops and add the bottoms.
What is the magnitude of the vector (6, 8)?
- 14
- 10 (the answer)
- 48
- 100
√(36 + 64).
What is 2 × the vector (3, −1)?
- (5, 1)
- (6, −1)
- (6, −2) (the answer)
- (3, −2)
Multiply both parts by 2.
A and B have position vectors a and b. What is the vector from A to B?
- a + b
- a − b
- b − a (the answer)
- ab
Go from A back to the origin (−a), then out to B (+b).
Which vector is parallel to (2, 3)?
- (3, 2)
- (4, 6) (the answer)
- (2, −3)
- (5, 6)
It is 2 × (2, 3).

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

3 questions, 6 marks. Write your answers on paper, then check them.

Vectors

Cambridge IGCSE Mathematics 0580 · 6 marks · papermunch.org

Name ______________________________ Date ______________

a has parts (2, 5) and b has parts (4, −1). Find a + b and 3a.[2]
Show answerHide answer
(6, 4) and (6, 15).
I got this one
Find the magnitude of the vector with parts (5, 12).[2]
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13.
I got this one
The position vectors of A and B are a and b. M is the midpoint of AB. Find the position vector of M.[2]
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½(a + b), or a + ½(b − a).
I got this one

Answers: Vectors

1. (6, 4) and (6, 15).
2. 13.
3. ½(a + b), or a + ½(b − a).