Chapter 9 Unit Test. Name: Section: Use v = 3.2i – 2.5j + 2.7k and w = 4.6i – 3.2j
– k to find: 1a) – 7v + 4w. 1b) ||v + w|| – 3||v||. Decompose v into two vectors, one ...
Chapter 10 Unit Test Name:
Section:
Use v = 3.2i – 2.5j + 2.7k and w = 4.6i – 3.2j – k to find: 1a)
– 7v + 4w
1b)
||v + w|| – 3||v||
Decompose v into two vectors, one parallel to w and the other orthogonal to w: 2) v = – 4.6i + 2.1j and w = 1.8i – 5.2j Given v and w, find a) v•w, b) the angle between v and w, and c) v×w: 3) v = – 5.2i – 2.3j + 6k and w = 3.7i + 1.9j – 3.4k Find the following: 4a)
Write the complex number z = 3 – ( 5 )i in polar form:
4b)
Use the result from part a to evaluate [3 – ( 5 )i]11. Write your final answer in rectangular form. €
€ in polar form: Find the following. Leave your answers z = 4.5(cos(234.5˚) + isin(234.5˚)) and w = 1.8(cos(84˚) + i sin(84˚)) 5a)
zw
5b)
z w
Transform the equation from polar to rectangular form: 6)
r=
4 1+sin(θ)
Find all complex roots. Write your answer in polar form with the argument in degrees: € 7) The complex fifth roots of – 4 – 7 i Solve the following: 8) Sailing a boat, Juanita maintains a constant speed of 25 nautical miles per hour bearing N45˚E. € If the current speed is 8 nautical miles per hour due North, find the actual speed and direction of the boat.
Write each complex number in standard form a + bi and graph the number on the complex plane (Be sure to label the axes): 9) 4.6(cos(135.3˚) + isin(135.3˚)) Find the direction angles of each vector and write the vector in the magnitude and direction angle form: 10) v = – 5.6i + 1.7j – 3.3k Given the following polar equation r = 1 – 3cos(θ): 11a) Determine which tests for symmetry the equation satisfies. Show your justification. 11b) Create an appropriate table of values and sketch the graph. Given the following polar equation r2 = 15sin(2θ): 12a) Determine which tests for symmetry the equation satisfies. Show your justification. 12b) Create an appropriate table of values and sketch the graph. Answers: 1a) – 4i + 4.7j – 22.9k 1b) ≈ – 4.820 2) v1 ≈ – 1.141i + 3.297j, v2 ≈ – 3.459i – 1.197j 3a) – 44.01 3b) 172.331˚ 3c) – 3.58i + 4.52j – 1.37k 4a) ≈
