Friday, 8 January
Math 105, section 207
Quiz 1
Name:
Student number:
Time: 10 minutes
Note: Each wrong answer has 13 negative score and each right answer has 1 positive
score. If you are not sure about a question, leave it blank.
−−→
1. LetP = (5, 11, 12) and Q = (1, 14, 13) be two points. Express P Q in terms of
i = h1, 0, 0i ,j = h0, 1, 0i and k = h0, 0, 1i:
a) -4i+3j+k
b) 4i+3j+k
c) 4i-3j-k
d) -4i-3j-k
2. Which of the following points is closer to the origin?
a) (1,1,-1)
b) (1,1,1)
c) (2,0,0)
d) (1,0,1)
3. Assume u = h4, −3, 0i and v = h0, 1, 1i. What is 4u − v?
a) h16, −11, 1i
b) h16, −13, −1i
c) h16, −11, −1i
d) h4, −1, 0i
4. Let u = 2i − 3k and v = i + 4j + 2k. What is u.v?
a) −1
b) −10
c) −4
d) h2, 0, −1i
5. Let u, v and w be three vectors such that u.v =
(2v − w).u :
a) 35
b) − 53
c) 65
d) 11
6
2
3
and u.w =
−1
2 .
Compute
6. What is the angle between vectors u = i + j and v = 3i − 3j?
a) π6
b) π4
c) π3
d) π2
7. Find α such that the vector u = h1, 2, α + 1i is orthogonal to v = h−3α, −5, 5i?
a) 32
b) 52
c) −1
d) 85