# Section 9.6 Vectors in the Plane

Education

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All Questions

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Q 1

Find vectors u and v whose initial and terminal points are given.Determine whether u and v are equivalent.
U: (6,5), (9,11)v: (3,-5), (6,1)
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C

Q 2

Find the vector v whose initial and terminal points are given below.
(5,5), (7,2)
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B

Q 3

Find the vector v whose initial and terminal points are given below.
(5)5,2.1), (9.5,6.1)
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D

Q 4

Given ,find .
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Q 5

Given and ,find .
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Q 6

Given and ,find .
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Q 7

The vector v and its initial point is given.Find the terminal point. ,initial point
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Q 8

Find the magnitude of the vector given below.Round your answer to four decimal places.
A)0
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Q 9

Find the unit vector in the direction of u.
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Q 10

Find the vector v with the given magnitude ||v|| = 185 and the same direction as .
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Q 11

Find the component form of vector v given its magnitude is and the angle it makes with the positive x-axis is .
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Q 12

Find the component form of vector u + v given and and the angles that u and v make with the positive x-axis are and .
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Multiple Choice

Q 13

Three forces with magnitudes 80 pounds,110 pounds and 25 pounds act on an object at angles 30°,-70°,and 120° respectively,with the positive x-axis.Find the direction and magnitude of the resultant force.(The choices below are given to two decimal places. )
A)136.12 pounds at angle of - 66.16° with the positive x-axis
B)103.21 pounds at angle of 23.84° with the positive x-axis
C)103.21 pounds at angle of - 66.16° with the positive x-axis
D)136.12 pounds at angle of - 23.84° with the positive x-axis
E)103.21 pounds at angle of - 23.84° with the positive x-axis

Multiple Choice

Q 14

Suppose a gun with a muzzle velocity of 1200 feet per second is fired at an angle of 4° above the horizontal.Find the horizontal component of the velocity.Round your answer to two decimal places.
A)1,240.08 ft/sec
B)2,395.15 ft/sec
C)1,197.08 ft/sec
D)2,393.15 ft/sec
E)1,209.08 ft/sec

Multiple Choice

Q 15

To carry a 100-pound cylindrical weight,two workers lift on the ends of short ropes tied to an eyelet on the top center of the cylinder.One rope makes a 20° angle away from the vertical and the other makes a 30° angle as shown in the figure below.Find each rope's tension if the resultant force is vertical.Round your answer to two decimal places.
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Q 16

To carry a 500-pound cylindrical weight,two workers lift on the ends of short ropes tied to an eyelet on the top center of the cylinder.One rope makes a 20° angle away from the vertical and the other makes a 30° angle as shown in the figure below.Find the vertical component of each worker's force.Round your answer to two decimal places.
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Multiple Choice

Q 17

Suppose a plane is flying in the direction 302°.Its speed with respect to the air is 900 kilometers per hour.The wind at the plane's altitude is from the southwest at 100 kilometers per hour (see figure).What is the true direction of the plane? Round your answer to two decimal places.
A)38.34° North of West
B)77.67° North of West
C)27.34° North of East
D)4.66° North of West
E)75.67° North of South

Multiple Choice

Q 18

Suppose a plane is flying in the direction 302° (relative to the west).Its speed with respect to the air is 600 kilometers per hour.The wind at the plane's altitude is from the southwest at 80 kilometers per hour (see figure).What is its speed with respect to the ground? Round your answer to one decimal place.
A)1,175.4 km/hr
B)587.2 km/hr
C)585.0 km/hr
D)962.4 km/hr
E)606.20 km/hr

Multiple Choice

Q 19

Suppose a plane flies at a constant groundspeed of 600 miles per hour due east and encounters a 10 mile-per-hour wind from the northwest.Both the airspeed and the compass direction must change to for the plane to maintain its groundspeed and eastward direction.Find the airspeed to maintain its groundspeed and eastward direction.Round your answer to two decimal places.
A)177.63°
B)131.32°
C)106.32°
D)89.32°
E)179.63°

Multiple Choice

Q 20

Suppose a plane flies at a constant groundspeed of 500 miles per hour due east and encounters a 50 mile-per-hour wind from the northwest.Both the airspeed and the compass direction must change to for the plane to maintain its groundspeed and eastward direction.Find the airspeed to maintain its groundspeed and eastward direction.Round your answer to two decimal places.
A)526.99 mi/h
B)507.99 mi/h
C)485.99 mi/h
D)643.99 mi/h
E)465.99 mi/h

Multiple Choice