D: LeftAngleBracket 9, 12 RightAngleBracket

Answers S1S-OC Pre-Calculus B E3710 - AGDot Product and Work

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Given u = ⟨2, –8⟩ and v = ⟨8, –2⟩, what is u · v?

–68

–60

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Let a = 2i + 9j, b = –4i + 5j, c = i – 3j, and d = 14j where i and j are unit vectors. What is (a – b) – (2d – c) in terms of i and j?

5i – 27j

5i + 35j

7i – 27j

7i + 39j

Let u =. What is 3u?

LeftAngleBracket 6, 7 RightAngleBracket

LeftAngleBracket 6, 12 RightAngleBracket

LeftAngleBracket 9, 7 RightAngleBracket

LeftAngleBracket 9, 12 RightAngleBracket

A force of 50 pounds acts in a direction 60° above horizontal, moving an object 100 feet from (0, 0) to (100, 0). How much work is done by the force?

25 foot-pounds

50 foot-pounds

2,500 foot-pounds

5,000 foot-pounds

Review the graph.

magnitude of and direction angle equal to approximately 40°

magnitude of and direction angle equal to approximately 50°

magnitude of and direction angle equal to approximately 40°

magnitude of and direction angle equal to approximately 50°

Let |r| = 6 at an angle of 30° and |s| = 11 at an angle of 225°. Which expression represents |r – s|?

StartRoot 6 squared + 11 squared minus 2 (6) (11) cosine (15 degrees) EndRoot

StartRoot 6 squared + 11 squared minus 2 (6) (11) cosine (45 degrees) EndRoot

StartRoot 6 squared + 11 squared minus 2 (6) (11) cosine (165 degrees) EndRoot

StartRoot 6 squared + 11 squared minus 2 (6) (11) cosine (255 degrees) EndRoot

A boat leaves a pier and travels 15 miles due east, then turns and travels 15 miles in the direction N 20° E. Which diagram represents the boat’s current distance, x, from the pier?

On a coordinate plane, a vector labeled 15 miles is on the x-axis. From that vector, another vector labeled 15 miles goes up and to the right. Vector x goes from (0, 0) to the terminal point of vector 15 miles. Angle a formed with a vertical line and vector 15 miles is 20 degrees.

On a coordinate plane, a vector labeled 15 miles is on the x-axis. From that vector, another vector labeled 15 miles goes up and to the left. Vector x goes from (0, 0) to the terminal point of vector 15 miles. Angle a formed by a vertical line and vector 15 miles is 20 degrees.

The speed of a boat in still water is 25 mph. The boat is traveling on a river with a current flowing south at 10 mph. At what angle upstream should the boat head to travel due west?

21.80°

23.58°

66.42°

68.20°

The magnitude of vector u is 34, and the magnitude of vector v is 20. The dot product u · v = –10. What is the approximate angle between the vectors?

79°

89°

91°

101°

Given vectors u = ⟨–2, 3⟩ and v = ⟨–6, 9⟩, what is the measure of the angle between u and v?

0°

86°

91°

180°

Review the graph.

(StartFraction 25 Over 2 EndFraction, StartFraction 25 StartRoot 3 EndRoot Over 2 EndFraction)

(StartFraction 25 Over 2 EndFraction, negative StartFraction 25 StartRoot 3 EndRoot Over 2 EndFraction)

(negative StartFraction 25 Over 2 EndFraction, StartFraction 25 StartRoot 3 EndRoot Over 2 EndFraction)

(negative StartFraction 25 Over 2 EndFraction, negative StartFraction 25 StartRoot 3 EndRoot Over 2 EndFraction)

Which diagram shows the parallelogram method for vector addition?

Vectors v and u share an origin. Vector v goes up and to the left, and vector u goes down and to the right. Vector u + v shares an origin with the terminal point of vector u, and shares a terminal point with the terminal point of vector v.

Vectors v and u share an origin. Vector v goes up and to the left, and vector u goes down and to the right. Vector u + v shares a terminal point with the terminal point of vector u, and shares an origin with the terminal point of vector v.

Vectors v and u share an origin. Vector v goes up and to the left, and vector u goes down and to the right. Vector u + v shares an origin with the vectors v and u and goes down and to the right.

Vectors v and u share an origin. Vector v goes up and to the left, and vector u goes down and to the right. Vector u + v shares an origin with the vectors v and u and goes down and to the right and is double the size of vectors v and u.

Review the diagram.

The horizontal is 150 pounds, and the vertical is 260 pounds.

The horizontal is 260 pounds, and the vertical is 150 pounds.

The horizontal is 346 pounds, and the vertical is 600 pounds.

The horizontal is 600 pounds, and the vertical is 346 pounds.

A cargo ship left port A and is headed across the ocean to shipping port B. After one month, the ship stopped at a refueling station along a path described by a vector with components . After another month, on the same path, the ship reached port B, twice the distance from port A as the fueling station.What are the characteristics of the vector representing the path of the ship?

components:, magnitude: 13.46

components:, magnitude: 53.85

components:, magnitude: 13.46

components:, magnitude: 53.85

A vector has initial point at (3, –5) and terminal point at (–2, 3). What are the characteristics of this vector?

The magnitude is , and the direction angle is about 58°.

The magnitude is , and the direction angle is about 122°.

The magnitude is , and the direction angle is about 58°.

The magnitude is , and the direction angle is about 122°.

Let |u| = 4 at an angle of 210° and |v| = 9 at an angle of 315°, and w = u – v. What is the magnitude and direction angle of w?

|w| = 5.5; θ = 156.1°

|w| = 5.5; θ = 203.9°

|w| = 10.8; θ = 156.1°

|w| = 10.8; θ = 203.9°

Review the graph.

less than –1

between –1 and 0

between 0 and 1

greater than 1

Let |r| = 17 at an angle of 40° and |s| = 14 at an angle of 160°. Which expression represents |r + s|?

StartRoot 17 squared + 14 squared minus 2 (17) (14) cosine (40 degrees) EndRoot

StartRoot 17 squared + 14 squared minus 2 (17) (14) cosine (60 degrees) EndRoot

StartRoot 17 squared + 14 squared minus 2 (17) (14) cosine (10 degrees) EndRoot

StartRoot 17 squared + 14 squared minus 2 (17) (14) cosine (120 degrees) EndRoot

Suppose vector u = , |v| = 6, and the angle between the vectors is 120°. What is u · v?

–8.19

–6

8.19

Let r = ⟨7, 1⟩, s = ⟨–6, 2⟩, and t = ⟨–9, –3⟩. What is 10r + s – t?

⟨55, 9⟩

⟨55, 15⟩

⟨73, 6⟩

⟨73, 15⟩

Review the diagram.

approximately 85 m

approximately 122 m

approximately 174 m

approximately 194 m

A hurricane was detected in the Atlantic around 5 a.m. The National Weather Service determined that it will make landfall at a location described by a vector with components . Around 6 a.m. on the same path, the hurricane is the total distance from where it was detected initially to where it will make landfall.If the hurricane is traveling on a straight path, what are the characteristics of the vector representing the path of the hurricane at 6 a.m.?