advertisement

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: