Spherical Trigonometry, Vectors, Complex Numbers (Workbook)

Question 1

Set 1 Problem 68: Find the angle between the vectors 3i + 2j + 5k and -4i + j + 6k.

Answer 1

63.53°

Question 2

Set 1 Problem 75: Evaluate the complex number ( 2∠30° )⁶.

Answer 2

-64 (p. 17)

Question 3

Set 2 Problem 49: An airplane flew from Sydney ( 151°12’ E, 33°52’ S ) on a course N 40° W maintaining a uniform altitude. At what longitude will it crosses the equator?

Answer 3

126°08’

Question 4

Set 3 Problem 8: Find the value of y if ( 2 + i ) divided by ( 1 - i ) equals i times ( x + yi ).

Answer 4

-1/2 (p. 42)

Question 5

Set 3 Problem 25: An airplane flew from Sydney (151°12’ E, 33°52’ S) on a course N 40° W and maintaining a uniform altitude. What is its distance from Sydney when it crosses the equator?

Answer 5

2,473.20 NM (p. 45)

Question 6

Set 3 Problem 45: Given the parts of an oblique spherical triangle: A=121°, B=29°, and a=136°. Compute side c.

Answer 6

127.41° (p.49)

Question 7

Set 3 Problem 68: Find the area of a triangle with vertices at P( 1, 4, 6 ), Q( -2, 5, -3 ) and R( 3, -1, 1 ).

Answer 7

30.65 (p. 54)

Question 8

Set 5 Problem 44: Evaluate: ( 1 - i )⁷.

Answer 8

8 + 8i

Question 9

Set 5 Problem 45: Evaluate: i^43 - i^-10.

Answer 9

1 - i

Question 10

Set 5 Problem 72: Find the cross product of the 2 vectors A = 3i - 4j + 6k and B = -2i + 8j + k.

Answer 10

-52i - 15j + 16k

Question 11

Set 6 Problem 48: Given the coordinates of 2 places: New York( 40°43’ N, 74° 0’ W ) and Liverpool( 53° 24’ N, 3° 4’ W ).
Find the distance between the 2 places, in nautical miles.

Answer 11

2,870 N.M.

Question 12

Set 6 Problem 49: Given the coordinates of 2 places: New York( 40°43’ N, 74° 0’ W ) and Liverpool( 53° 24’ N, 3° 4’ W ).
Find the bearing of Liverpool from New York..

Answer 12

N 49° 30’ E

Question 13

Set 6 Problem 50: Given the coordinates of 2 places: New York( 40°43’ N, 74° 0’ W ) and Liverpool( 53° 24’ N, 3° 4’ W ).
Find the bearing of New York from Liverpool.

Answer 13

N 75°08’ W (p. 102)

Question 14

Set 6 Problem 66: Compute the magnitude of the vector F = 2i - 5k + 8k.

Answer 14

9.64

Question 15

Set 6 Problem 75: Given the 2 vectors A = 2i + 4j and B = ai + bj. Find the value of a if A x B = 0 and A *B = 30.

Answer 15

3 (p. 106)

Question 16

Set 7 Problem 34: Find the angle between the vectors, A = 2i - j + 2k and B = 6i + 3j + k.

Answer 16

57.27°

Question 17

Set 8 Problem 4: A spherical triangle has the following parts: B = 118°, c = 82°, and a = 54°. Compute b.

Answer 17

107.12°

Question 18

Set 8 Problem 33: Given a right spherical triangle with C = 90°, a = 72°27’, and b = 61°49’.
Find c.

Answer 18

81°49’

Question 19

Set 8 Problem 34: Given a right spherical triangle with C = 90°, a = 72°27’, and b = 61°49’.
Find A.

Answer 19

74°25’

Question 20

Set 8 Problem 35: Given a right spherical triangle with C = 90°, a = 72°27’, and b = 61°49’.
Find the area of the spherical triangle if the radius of the sphere is 10 m.

Answer 20

82.64 m^2

Question 21

Set 9 Problem 5: The cross product of two vectors A=6i+8j and B=xi-4j is zero. Find the value of x.

Answer 21

-3 (p.145)

Question 22

Set 9 Problem 29: A right spherical triangle has the following parts: C = 90°, a = 40°, and b = 80°. Find the measure of angle B.

Answer 22

83°32’

Question 23

Set 9 Problem 55: Compute angle A of a spherical triangle whose parts are: a = 58°, b = 112°, c = 70°.

Answer 23

40°57’