Vectors in 3 Dimensions (OCR A Level Maths A): Revision Note

Vectors in 3 dimensions

What is a 3D vector?

• Vectors represent a movement of a certain magnitude (size) in a given direction

  You should have already come across (2D) vectors at AS (see Basic Vectors)

• 3D vectors describe the position of a point in a 3D 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 3D vector

• The magnitude of a 3D vector is simply its size

• Like 2D vectors we can find the magnitude using Pythagoras’ theorem (see Magnitude Direction)

• For 3D 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:

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

• 3D vectors work in the same way as 2D 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

• 3D vectors are also parallel if one is a multiple of the other

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