NAME:
MATH 151
September 10, 2014
QUIZ 1
• Calculators are NOT allowed!
• Show all your work and indicate your final answer clearly. You will be graded not merely
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