 # Length of a Vector

In this worksheet, students work out the modulus or size of a coordinate vector using Pythagoras' Theorem. Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Curriculum subtopic:  Describe Translations as 2D Vectors

Difficulty level:   ### QUESTION 1 of 10

To find the "modulus" or "absolute value" or size or length of a vector, we imagine it drawn on a set of coordinate axes and use Pythagoras' Theorem to calculate its size.

Example

Calculate the length of the following vector to 3 sig. figs.:

 ( -6 ) 5

We picture the vector as a horizontal and vertical shift. By Pythagoras' Theorem, we get:

a2 = 62 + 52

a2 = 36 + 25

a2 = 61

a = √61 = 7.810249...

a ≈ 7.81 (3sf)

Calculate the length of the following vector to 3 sig. figs.:

 ( 3 ) 5

Calculate the length of the following vector to 3 sig. figs.:

 ( 4 ) 5

Calculate the length of the following vector to 3 sig. figs.:

 ( 6 ) 2

Calculate the length of the following vector to 3 sig. figs.:

 ( 1 ) 7

Calculate the length of the following vector to 3 sig. figs.:

 ( 4 ) 10

Calculate the length of the following vector to 3 sig. figs.:

 ( -3 ) 5

Calculate the length of the following vector to 3 sig. figs.:

 ( 7 ) -5

Calculate the length of the following vector to 3 sig. figs.:

 ( -6 ) 10

Calculate the length of the following vector to 3 sig. figs.:

 ( 11 ) -2

Calculate the length of the following vector to 3 sig. figs.:

 ( -8 ) -9

• Question 1

Calculate the length of the following vector to 3 sig. figs.:

 ( 3 ) 5

5.83
EDDIE SAYS
a² = 3² + 5²
• Question 2

Calculate the length of the following vector to 3 sig. figs.:

 ( 4 ) 5

6.40
EDDIE SAYS
a² = 4² + 5²
• Question 3

Calculate the length of the following vector to 3 sig. figs.:

 ( 6 ) 2

6.32
EDDIE SAYS
a² = 6² + 2²
• Question 4

Calculate the length of the following vector to 3 sig. figs.:

 ( 1 ) 7

7.07
EDDIE SAYS
a² = 1² + 7²
• Question 5

Calculate the length of the following vector to 3 sig. figs.:

 ( 4 ) 10

10.8
EDDIE SAYS
a² = 4² + 10²
• Question 6

Calculate the length of the following vector to 3 sig. figs.:

 ( -3 ) 5

5.83
EDDIE SAYS
a² = (-3)² + 5²
• Question 7

Calculate the length of the following vector to 3 sig. figs.:

 ( 7 ) -5

8.60
EDDIE SAYS
a² = 7² + (-5)²
• Question 8

Calculate the length of the following vector to 3 sig. figs.:

 ( -6 ) 10

11.7
EDDIE SAYS
a² = (-6)² + 10²
• Question 9

Calculate the length of the following vector to 3 sig. figs.:

 ( 11 ) -2

11.2
EDDIE SAYS
a² = 11² + (-2)²
• Question 10

Calculate the length of the following vector to 3 sig. figs.:

 ( -8 ) -9