# NAME: MATH 151 September 10, 2014 QUIZ 1 ```NAME:
MATH 151
September 10, 2014
QUIZ 1
• Calculators are NOT allowed!
on the final answer, but also on the work leading up to it.
1. (3 points) Find a unit vector that has the same direction as v = 5i + 12j.
√
√
Solution: The magnitude of the vector v is 52 + 122 = 169 = 13. Thus the unit vector
that has the same direction as v is
v
5
12
= i + j.
|v|
13
13
2. (3 points) Find all values of x in the interval [0, 2π] that satisfy:
2 cos x − 1 = 0.
Solution: Solving for cos x gives that we want to find the x in [0, 2π] such that
1
cos x = .
2
π 5π
The x that satisfy this are x = 3 , 3 .
Note that cos 2π
= − 21 and cos 4π
= − 12
3
3
NAME:
MATH 151
September 10, 2014
3. (3 points) Find the equation of the line that passes through the point (−3, −5), and is
perpendicular to the line 5x + 2y + 8 = 0.
Solution: The equation 5x + 2y + 8 = 0 can be rewritten as y = − 52 x − 4 and so the
slope of the given line is − 52 . Then the slop of the line perpendicular to y is 52 . The line
perpendicular to the given line is then y⊥ = 52 x + b. Since the point (−3, −5) lies on this
line, then −5 = 25 (−3) + b and so b = − 19
. The equation of the line perpendicular to the
5
given line passing through (−3, −5) is then
2
19
y⊥ = x − .
5
5
```