Cambridge International AS and A Level Mathematics Pure Mathematics 1

Vectors

P1^

8

Adding  vectors is  like    adding  the legs    of  a   journey to  find    its overall outcome (see    

figure  8.14).

When    vectors are given   in  magnitude−direction form,   you can find    their   

resultant   by  making  a   scale   drawing,    as  in  figure  8.14.   If, however,    you need    

to  calculate   their   resultant,  it  is  usually easiest to  convert the vectors into    

component   form,   add component   by  component,  and then    convert the answer  

back    to  magnitude−direction form.

Subtracting vectors

Subtracting one vector  from    another is  the same    as  adding  the negative    of  the 

vector.

ExamPlE 8.8  Two    vectors a   and b   are given   by

a =     2 i +   3 j b = −i +    2 j.

(i) Find    a − b.  

(ii)    Draw    diagrams    showing a,  b,  a − b.

SOlUTION

(i) a − b = (2i +   3j) −   (−i +   2j)

=   3 i +   j

(ii)

resultant

leg 2

leg 1

leg 3

Figure 8.14

a

–b

a + (–b) = a – b

j

i

b

a

Figure 8.15