Quiz #2
Answers
September 8, 2015
Math 251
You will be graded on both the correct answer and the correctness of the work that you provide to justify that
answer. I expect to see all of your work in a neat and orderly manner. If you want, you may work the problems
on other paper and turn in all your work.
1. Let a = h1, 2, 7i and b = h0, −4, 2i.
(a) Find b × a
i
b × a = 0
1
j
−4
2
k
2
7
= h−32, 2, 4i
(b) Find a unit vector that is orthogonal to the vectors a and b.
−32
2
4
√
,√
,√
1044
1044
1044
2. Find the equation of the plane that contains these lines.
r1 (t) = h1 + t, 1 − t, 2ti
r2 (s) = h2 − s, s, 2i
First check to see if the lines are skew. They actually intersect when t = 1 and s = 0 at the point (2, 0, 2).
The directional vectors of the lines are v1 = h1, −1, 2i, and v2 = h−1, 1, 0i.
The the normal vector to the plane be n = v1 × v2 = h−2, −2, 0i
Answer: −2(x − 2) − 2(y − 0) + 0(z − 2) = 0 or −2x − 2y = −4.