What is a 3-D vector?

• Vectors represent a movement of a certain?magnitude?(size) in a given?directionYou should have already come across (2D)?vectors?at AS (see Basic Vectors)
• 3-D vectors describe the?position of a point?in a 3-D space in relation to the?origin
• They can be represented in different ways such as a?column vector?or in?i, j, k unit vector form

Magnitude of a 3-D vector

• The magnitude of a 3-D vector is simply its size
• Like 2-D vectors we can find the?magnitude?using Pythagoras’ theorem (see Magnitude Direction)

• For 3-D?position vectors?we can find the distance between two points
• By using the respective co-ordinates we can calculate the magnitude of the vector between them:

3-D vector addition, scalars, parallel vectors and unit vectors

• 3-D vectors work in the same way as 2-D vectors, just in three dimensions rather than two
• Vector addition?and subtraction and scalar multiplication can be carried out in exactly the same way, this time involving?i, j?and?k?or x, y and z
• 3-D vectors are also?parallel?if one is a?multiple?of the other

• Unit vectors?in 3-D are found in exactly the same way as in 2-D