Cambridge International AS and A Level Mathematics Pure Mathematics 1

Vectors

P1^

8

Vectors in three dimensions

Points

In  three   dimensions, a   point   has three   co-ordinates,   usually called  x,  y   and z.

The axes    are conventionally  arranged    as  shown   in  figure  8.8,    where   the point   P   is  

(3, 4,  1). Even    on  correctly   drawn   three-dimensional   grids,  it  is  often   hard    to  see 

the relationship    between the points, lines   and planes, so  it  is  seldom  worth   your    

while   trying  to  plot    points  accurately.

The unit    vectors i,  j   and k   are used    to  describe    vectors in  three   dimensions.

z

2

1

–1

–1

1

2

3

2 3

P

4 y

x

–3 –2 –1 O 1

Figure 8.8

This point is

(3, 4, 1).