Math 273
Quiz 3
Name:
29 Jan 2016
Show appropriate work.
Point Values in boxes - Scaled to 10 .
1. 4 Please indicate True or False. Assume the vectors u and v are non-zero.
(a) T / F : u × u = 0
(b) T / F : kukv + u⊥v k = kuk
(c) T / F : The plane 2x + y − 3z = 0 passes through the point (2, 1, −3).
(d) T / F : k × (−j) = i
2. 4 Find the decomposition of u =< 4, −7, 1 > along v =< 2, 3, −1 >, i.e. find ukv and u⊥v .
3. 6 Find an equation of the plane containing the points P = (1, 2, 3), Q = (2, 0, 1), and R = (3, 2, 1).
4. 4 Provide a reasonably clear sketch of the following traces for the quadric surface x2 +4y 2 = z 2 +1
in the specified planes.
(a) xy-plane
(c) xz-plane
(b) yz-plane
(d) z =
√
3
5. 2 Based on the traces you found above, identify the graph of x2 + 4y 2 = z 2 + 1 from the choices
below by circling the Figure number.
Figure 1:
Figure 2:
Figure 3:
Figure 4:
Figure 5:
Figure 6: