# Vector Addition and Subtraction of Multiples

In this worksheet, students add and subtract multiples of simple 2D vectors.

Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Difficulty level:

### QUESTION 1 of 10

A vector is a "carrier" of information regarding a shifting movement.

A 2D vector can be written in the form

 ( x ) y

where x is the horizontal shift and y is the vertical shift.

The following diagram shows how a positive of negative number affects the direction of the shift.

To add or subtract vectors, we add or subtract the top numbers and the bottom numbers separately.

To find multiples of vectors, we simply multiply the top and bottom numbers by the multiple.

Example 1

Work out:

 ( 3 ) + 2 ( -2 ) 5 6

 ( 3 + -4 ) 5 + 12

 ( -1 ) 17

Example 2

Work out:

 4 ( 3 ) - ( -2 ) -5 6

 ( 12 - -2 ) -20 - 6

 ( 14 ) -26

 ( 3 ) + 2 ( -2 ) 4 3

 1 ( -1 ) 2. ( 4 ) 3. ( -1 ) 10 10 7

1.

2.

3.

 2 ( 3 ) + ( -2 ) 4 3

 1 ( -1 ) 2. ( 4 ) 3. ( -1 ) 10 11 7

1.

2.

3.

 3 ( 3 ) + ( 4 ) -1 -1

 1 ( 13 ) 2. ( 7 ) 3. ( 13 ) -2 -2 -4

1.

2.

3.

 ( 3 ) - 2 ( 4 ) -1 -1

 1 ( 11 ) 2. ( 7 ) 3. ( -5 ) -2 -3 1

1.

2.

3.

 ( 3 ) - ( 4 ) -1 -1

 1 ( -1 ) 2. ( -1 ) 3. ( -7 ) 0 -2 -2

1.

2.

3.

 3 ( 3 ) - 2 ( 4 ) -1 -1

 1 ( 13 ) 2. ( 1 ) 3. ( 13 ) -2 -1 -4

1.

2.

3.

 2 ( -5 ) - 3 ( 1 ) 0 -1

 1 ( -13 ) 2. ( 1 ) 3. ( 13 ) 3 -2 -3

1.

2.

3.

 3 ( -4 ) - ( 4 ) 1 -2

 1 ( -16 ) 2. ( 0 ) 3. ( -16 ) 1 -1 5

1.

2.

3.

 3 ( 4 ) + 2 ( 2 ) -1 -3

 1 ( 14 ) 2. ( 16 ) 3. ( -16 ) -4 -9 -7

1.

2.

3.

 4 ( -2 ) - 2 ( -2 ) -1 -1

 1 ( 4 ) 2. ( -8 ) 3. ( -4 ) -4 2 -2

1.

2.

3.

• Question 1

 ( 3 ) + 2 ( -2 ) 4 3

 1 ( -1 ) 2. ( 4 ) 3. ( -1 ) 10 10 7

1.
• Question 2

 2 ( 3 ) + ( -2 ) 4 3

 1 ( -1 ) 2. ( 4 ) 3. ( -1 ) 10 11 7

2.
• Question 3

 3 ( 3 ) + ( 4 ) -1 -1

 1 ( 13 ) 2. ( 7 ) 3. ( 13 ) -2 -2 -4

3.
• Question 4

 ( 3 ) - 2 ( 4 ) -1 -1

 1 ( 11 ) 2. ( 7 ) 3. ( -5 ) -2 -3 1

3.
• Question 5

 ( 3 ) - ( 4 ) -1 -1

 1 ( -1 ) 2. ( -1 ) 3. ( -7 ) 0 -2 -2

1.
• Question 6

 3 ( 3 ) - 2 ( 4 ) -1 -1

 1 ( 13 ) 2. ( 1 ) 3. ( 13 ) -2 -1 -4

2.
• Question 7

 2 ( -5 ) - 3 ( 1 ) 0 -1

 1 ( -13 ) 2. ( 1 ) 3. ( 13 ) 3 -2 -3

1.
• Question 8

 3 ( -4 ) - ( 4 ) 1 -2

 1 ( -16 ) 2. ( 0 ) 3. ( -16 ) 1 -1 5

3.
• Question 9

 3 ( 4 ) + 2 ( 2 ) -1 -3

 1 ( 14 ) 2. ( 16 ) 3. ( -16 ) -4 -9 -7

2.
• Question 10

 4 ( -2 ) - 2 ( -2 ) -1 -1

 1 ( 4 ) 2. ( -8 ) 3. ( -4 ) -4 2 -2