12.1 - 12.2
Name:
1. Sketch the points A(−3, 0, −1), B(5, 1, −2), and C(2, 3, 5). Which is closest to the yz-plane? Which
point lies in the xz-plane?
2. Show that the following equation represents a sphere, and find its center and radius:
x2 + y 2 + z 2 − 2x + 8z = 19
3. Describe in words and sketch (if you can) the region of R3 represented by the equations or inequalities:
(a) x < 4
(b) y 2 = 1
(c) x2 + z 2 = 16
4. Find a unit vector that has the same direction as the given vector:
(a) −3i + 7j
(b) 8i − j + 4k
12.1 - 12.2
Name:
5. Write an inequality to describe the solid upper hemisphere of the sphere of radius 2 centered at the
origin.
6. Write each combination of vectors as a single vector.
−−→ −−→
(a) AB + BC
−−→ −−→
(c) DB − AB
−−→ −−→
(b) CD + DB
−−→ −→ −−→
(d) DC + CA + AB
7. Find a vector that has the same direction as h−3, −1, 2i but has length 6.
8. Carolyn drives her car north at 30 km/hr for 1 hour, east at 60 km/hr for 2 hours, then north at 50
km/hr for 1 hour. What is Carolyn’s net displacement?