The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Length of a Vector

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

'Length of a Vector' worksheet

Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Curriculum subtopic:  Describe Translations as 2D Vectors

Difficulty level:  

down

Worksheet Overview

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

 

Answer

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

 

CORRECT ANSWER
5.83
EDDIE SAYS
a² = 3² + 5²
  • Question 2

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

 

( 4 )
5

 

CORRECT ANSWER
6.40
EDDIE SAYS
a² = 4² + 5²
  • Question 3

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

 

( 6 )
2

 

CORRECT ANSWER
6.32
EDDIE SAYS
a² = 6² + 2²
  • Question 4

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

 

( 1 )
7

 

CORRECT ANSWER
7.07
EDDIE SAYS
a² = 1² + 7²
  • Question 5

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

 

( 4 )
10

 

CORRECT ANSWER
10.8
EDDIE SAYS
a² = 4² + 10²
  • Question 6

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

 

( -3 )
5

 

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

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

 

( 7 )
-5

 

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

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

 

( -6 )
10

 

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

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

 

( 11 )
-2

 

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

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

 

( -8 )
-9

 

CORRECT ANSWER
12.0
EDDIE SAYS
a² = (-8)² + (-9)²
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Start your £1 trial

Start your trial for £1