136 STEP 4. Review the Knowledge You Need to Score High
- The path of an object is defined byx= 2 t,y=t+1. Find the location of the object
whent=5.
Answer:Whent=5,x=2(5)=10 andy= 5 + 1 =6 so the location
is (10, 6). - Identify the shape of each equation: (a)r=
θ
5
; (b)r=6 cos 3θ
Answers:(a) spiral, (b) rose- Find the magnitude of the vector
〈
1,−√
3〉
and the angle it makes with the positive
x-axis.Answers:Magnitude=√
12 +(−√
3)^2 =√
1 + 3 =2.Angle=tan−^1(
−√
3
1)
=
−π
3.
- Ifa=〈4,− 2 〉,b=〈−3, 1〉, andc=〈0, 5〉, find 3a− 2 b+c.
Answer: 3 〈4,− 2 〉− 2 〈−3, 1〉+〈0, 5〉=〈12,− 6 〉+〈6,− 2 〉+〈0, 5〉=〈18,− 8 〉+
〈0, 5〉=〈18,− 3 〉.