Example 6 Self Tutor
For points P, Q, R and S, simplify the following vector expressions:
a¡!
QR¡
¡!
SR b¡!
QR¡
¡!
SR¡
¡!
PS
a¡!
QR¡
¡!
SR
=
¡!
QR+
¡!
RS fas¡!
RS=¡
¡!
SRg
=¡!
QS
b¡!
QR¡
¡!
SR¡
¡!
PS
=
¡!
QR+
¡!
RS+
¡!
SP
=
¡!
QP
Example 7 Self Tutor
Xiang Zhu is about to fire an arrow at a target. In still conditions,
the arrow would travel at 18 m/s. Today, however, there is a wind
of 6 m/s blowing from the left directly across the arrow’s path.
a In what direction should Zhu fire the arrow?
b What will be its actual speed?Suppose Zhu is at Z and the target is at T. Letabe the arrow’s velocity in still conditions,wbe the
velocity of the wind, andxbe the vector¡!
ZT.
Now a+w=x
) a+w¡w=x¡w
) a=x¡w
a Now jaj=18m/s and jwj=6m/s
) sinμ= 186 =^13
) μ= sin¡^1¡ 1
3¢
¼ 19 : 47 o
) Zhu should fire about 19 : 5 oto the left of the target.
b By Pythagoras’ theorem, jxj^2 +6^2 =18^2
) jxj=p
182 ¡ 62 ¼ 16 : 97 m/s
) the arrow will travel at about 17 : 0 m/s.EXERCISE 24D
1 For the following vectorspandq, show how to construct p¡q:
abcQRSQSRPpqp
qpqxwqaTZ186q||¡¡x490 Vectors (Chapter 24)IGCSE01
cyan magenta yellow black(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_24\490IGCSE01_24.CDR Monday, 27 October 2008 2:26:49 PM PETER