Cambridge International AS and A Level Mathematics Pure Mathematics 1

Exercise

(^8)
a
261
P1^
8
●^ Show^ that^ the^ length^ of^ the^ three-dimensional^ vector^ a 1 i^ +^ a 2 j^ +^ a 3 k^ is^ given^ by
| a | = aa^21 + + 22 a 32.
ExamPlE 8.6 Find the magnitude of the vector a =

2

5

3

−

















.

SOlUTION

| a | =+ −+

=+ +

=

=

25 3

4259

38

616

(^22) () 2
.(to2d.p.)
ExERCISE  8 a   1  Express the following vectors in component form.
(i) (ii)
(iii) (iv)
2  Draw diagrams to show these vectors and then write them in magnitude−
direction form.
(i) 2 i + 3 j (ii) 3

• 2









(iii) –

• 
  

4

4









(iv) −i +   2 j (v)     3 i −   4 j

3  Find the magnitude of these vectors.

(i)

1

2

3

–

















(ii)

4

0

− 2

















(iii)   2 i +   4 j +   2 k

(iv) i + j −    3 k (v)

6

2

3

–

−















^

(vi) i −    2 k

y

3

a

2

1

–2

–1

–2 –1 0 1 2 3 4 x

y

3

 b



±

±

± ±   3 x

y

3

2 c

1

(^0) 1 2 3 4 x
y
3
2 d
1
(^012) 3 4 x