3.9.3 Magnitude of a Vector

How do you find the magnitude of a vector?

• The magnitude of a vector tells us its size or length
• For a displacement vector it tells us the distance between the two points
• For a position vector it tells us the distance of the point from the origin
• The magnitude of the vector is denoted 
• The magnitude of the vector a is denoted |a|
• The magnitude of a vector can be found using Pythagoras’ Theroem
• The magnitude of a vector  is found using
• 
• where 
• This is given in the formula booklet

How do I find the distance between two points?

• Vectors can be used to find the distance (or displacement) between two points
• It is the magnitude of the vector between them
• Given the position vectors of two points:
• Find the displacement vector between them
• Find the magnitude of the displacement vector between them

What is a unit vector?

• A unit vector has a magnitude of 1
• It can be found by dividing a vector by its magnitude
• This will result in a vector with a size of 1 unit in the direction of the original vector
• A unit vector in the direction of a is denoted 
• For example a unit vector in the direction 3i – 4j is