288 Vectors (Chapter 11)
Example 7 Self Tutor
If p=3i¡ 5 j and q=¡i¡ 2 j, find jp¡ 2 qj.
p¡ 2 q=3i¡ 5 j¡2(¡i¡ 2 j)
=3i¡ 5 j+2i+4j
=5i¡j
) jp¡ 2 qj=
p
52 +(¡1)^2
=
p
26 units
EXERCISE 11C
1 If a=
μ
¡ 3
2
¶
, b=
μ
1
4
¶
, and c=
μ
¡ 2
¡ 5
¶
find:
a a+b b b+a c b+c d c+b
e a+c f c+a g a+a h b+a+c
2 Given p=
μ
¡ 4
2
¶
, q=
μ
¡ 1
¡ 5
¶
, and r=
μ
3
¡ 2
¶
find:
a p¡q b q¡r c p+q¡r
d p¡q¡r e q¡r¡p f r+q¡p
3 Consider a=
μ
a 1
a 2
¶
.
a Use vector addition to show that a+ 0 =a.
b Use vector subtraction to show that a¡a= 0.
4 For p=
μ
1
5
¶
, q=
μ
¡ 2
4
¶
, and r=
μ
¡ 3
¡ 1
¶
find:
a ¡ 3 p b^12 q c 2 p+q d p¡ 2 q
e p¡^12 r f 2 p+3r g 2 q¡ 3 r h 2 p¡q+^13 r
5 Consider p=
μ
1
1
¶
and q=
μ
2
¡ 1
¶
. Find geometrically and then comment on the results:
a p+p+q+q+q b p+q+p+q+q c q+p+q+p+q
6 For r=
μ
2
3
¶
and s=
μ
¡ 1
4
¶
find:
a jrj b jsj c jr+sj d jr¡sj e js¡ 2 rj
7 If p=
μ
1
3
¶
and q=
μ
¡ 2
4
¶
find:
a jpj b j 2 pj c j¡ 2 pj d j 3 pj e j¡ 3 pj
f jqj g j 4 qj h j¡ 4 qj i
̄
̄^1
2 q
̄
̄ j
̄
̄¡^1
2 q
̄
̄
VECTOR RACE
GAME
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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_11\288CamAdd_11.cdr Monday, 6 January 2014 9:55:44 AM BRIAN