Multiple ChoiceDetermine if the following statement is true or false: Temperature is a vector. 86views
Multiple ChoiceDetermine if the following statement is true or false: Acceleration is a vector. 93views
Multiple ChoiceDetermine if the following statement is true or false: The vectors vvv and −v-v−v point in the same direction.96views
Multiple ChoiceGiven vectors u⃗u ⃗u⃗ and v⃗v ⃗v⃗, sketch the resultant vector u⃗+v⃗u ⃗+v ⃗u⃗+v⃗91views
Multiple ChoiceGiven vectors u⃗u ⃗u⃗ and v⃗v ⃗v⃗, sketch the resultant vector u⃗−v⃗u ⃗-v ⃗u⃗−v⃗.107views
Multiple ChoiceGiven vectors u⃗u ⃗u⃗ and v⃗v ⃗v⃗, sketch the resultant vector 12u⃗+v⃗\frac12u⃗+v⃗21u⃗+v⃗.79views
Multiple ChoiceGiven vectors u⃗u ⃗u⃗ and v⃗v ⃗v⃗, sketch the resultant vector −2u⃗+3v⃗-2u ⃗+3v ⃗−2u⃗+3v⃗.83views
Textbook QuestionIn Exercises 1–4, u and v have the same direction. In each exercise: Find ||u||. 179views
Textbook QuestionIn Exercises 1–4, u and v have the same direction. In each exercise: Is u = v? Explain.154views
Textbook QuestionIn Exercises 1–4, u and v have the same direction. In each exercise: Find ||v||.161views
Textbook QuestionIn Exercises 1–4, u and v have the same direction. In each exercise: Find ||u||.149views
Textbook QuestionIn Exercises 1–4, u and v have the same direction. In each exercise: Is u = v? Explain.154views
Textbook QuestionIn Exercises 1–4, u and v have the same direction. In each exercise: Find ||v||. 167views
Textbook QuestionIf P₁ = (-2, 3), P₂ = (-1, 5), and v is the vector from P₁ to P₂, Write v in terms of i and j.165views
Textbook QuestionIn Exercises 5–12, sketch each vector as a position vector and find its magnitude. v = 3i + j145views
Textbook QuestionIn Exercises 5–8, let v = -5i + 2j and w = 2i - 4j Find the specified vector, scalar, or angle. 3v - 4w148views
Textbook QuestionIn Exercises 5–12, sketch each vector as a position vector and find its magnitude. v = i - j171views
Textbook QuestionWrite each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.<IMAGE>113views
Textbook QuestionWrite each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.<IMAGE>118views
Textbook QuestionWrite each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.<IMAGE>127views
Textbook QuestionWrite each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.<IMAGE>123views
Textbook QuestionSolve each problem. See Examples 5 and 6.Distance and Direction of a Motorboat A motorboat sets out in the direction N 80° 00′ E. The speed of the boat in still water is 20.0 mph. If the current is flowing directly south, and the actual direction of the motorboat is due east, find the speed of the current and the actual speed of the motorboat.<IMAGE>139views
Textbook QuestionIn Exercises 5–12, sketch each vector as a position vector and find its magnitude. v = -6i - 2j152views
Textbook QuestionIn Exercises 5–12, sketch each vector as a position vector and find its magnitude. v = -4i141views
Textbook QuestionIn Exercises 13–20, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j. P₁ = (-4, -4), P₂ = (6, 2)181views
Textbook QuestionIn Exercises 13–20, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j. P₁ = (-8, 6), P₂ = (-2, 3)225views
Textbook QuestionIn Exercises 13–20, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j. P₁ = (-1, 7), P₂ = (-7, -7)170views
Textbook QuestionIn Exercises 13–20, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j. P₁ = (-3, 4), P₂ = (6, 4)196views
Textbook QuestionIn Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar. u + v157views
Textbook QuestionIn Exercises 22–24, sketch each vector as a position vector and find its magnitude. v = -3i - 4j152views
Textbook QuestionIn Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar. u - v141views
Textbook QuestionIn Exercises 22–24, sketch each vector as a position vector and find its magnitude. v = -3j152views
Textbook QuestionIn Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar. v - u142views
Textbook QuestionIn Exercises 25–26, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j. P₁ = (2, -1), P₂ = (5, -3)148views
Textbook QuestionIn Exercises 25–26, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j. P₁ = (-3, 0), P₂ = (-2, -2)167views
Textbook QuestionIn Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar. 5v146views
Textbook QuestionIn Exercises 27–30, let v = i - 5j and w = -2i + 7j. Find each specified vector or scalar. w - v163views
Textbook QuestionIn Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar. -4w155views
Textbook QuestionIn Exercises 27–30, let v = i - 5j and w = -2i + 7j. Find each specified vector or scalar. ||-2v||162views
Textbook QuestionIn Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar. 3w + 2v134views
Textbook QuestionIn Exercises 31–32, find the unit vector that has the same direction as the vector v. v = -i + 2j178views
Textbook QuestionIn Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar. 3v - 4w150views
Textbook QuestionIn Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar. ||2u||160views
Textbook QuestionIn Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar. ||w - u||174views
Textbook QuestionIn Exercises 39–46, find the unit vector that has the same direction as the vector v. v = 6i160views
Textbook QuestionIn Exercises 39–46, find the unit vector that has the same direction as the vector v. v = 3i - 4j173views
Textbook QuestionIn Exercises 39–46, find the unit vector that has the same direction as the vector v. v = 3i - 2j365views
Textbook QuestionIn Exercises 39–46, find the unit vector that has the same direction as the vector v. v = i + j245views
Textbook QuestionIn Exercises 47–52, write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given. ||v|| = 6, θ = 30°248views
Textbook QuestionIn Exercises 47–52, write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given. ||v|| = 12, θ = 225°165views
Textbook QuestionIn Exercises 47–52, write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given. ||v|| = 1/2, θ = 113°191views
Textbook QuestionIn Exercises 53–56, let u = -2i + 3j, v = 6i - j, w = -3i. Find each specified vector or scalar. 4u - (2v - w)158views
Textbook QuestionIn Exercises 53–56, let u = -2i + 3j, v = 6i - j, w = -3i. Find each specified vector or scalar. ||u + v||² - ||u - v||²182views
Textbook QuestionIn Exercises 61–64, find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v. v = -10i + 15j138views
Textbook QuestionIn Exercises 61–64, find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v. v = (4i - 2j) - (4i - 8j)153views
Textbook QuestionUse the figure to find each vector: u + v. Use vector notation as in Example 4.<IMAGE> 131views
Textbook QuestionUse the figure to find each vector: u - v. Use vector notation as in Example 4.<IMAGE> 130views
Textbook QuestionUse the figure to find each vector: - u. Use vector notation as in Example 4.<IMAGE> 133views
Textbook QuestionUse the figure to find each vector: u + v. Use vector notation as in Example 4.<IMAGE> 122views
Textbook QuestionUse the figure to find each vector: u - v. Use vector notation as in Example 4.<IMAGE> 126views
Textbook QuestionUse the figure to find each vector: - u. Use vector notation as in Example 4.<IMAGE> 126views
Textbook QuestionUse the figure to find each vector: u + v. Use vector notation as in Example 4.<IMAGE>114views
Textbook QuestionUse the figure to find each vector: u - v. Use vector notation as in Example 4.<IMAGE> 109views
Textbook QuestionUse the figure to find each vector: - u. Use vector notation as in Example 4.<IMAGE> 126views
Textbook QuestionFind the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary.〈15, -8〉128views
Textbook QuestionFind the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary.〈-4, 4√3〉121views
Textbook QuestionRefer to vectors a through h below. Make a copy or a sketch of each vector, and then draw a sketch to represent each of the following. For example, find a + e by placing a and e so that their initial points coincide. Then use the parallelogram rule to find the resultant, as shown in the figure on the right.<IMAGE>a + (b + c)143views
Textbook QuestionRefer to vectors a through h below. Make a copy or a sketch of each vector, and then draw a sketch to represent each of the following. For example, find a + e by placing a and e so that their initial points coincide. Then use the parallelogram rule to find the resultant, as shown in the figure on the right.<IMAGE>c + d141views
Textbook QuestionVector v has the given direction angle and magnitude. Find the horizontal and vertical components.θ = 50°, |v| = 26173views
Textbook QuestionVector v has the given direction angle and magnitude. Find the horizontal and vertical components.θ = 27° 30' |v| = 15.4124views
Textbook QuestionFor each pair of vectors u and v with angle θ between them, sketch the resultant.|u| = 12, |v| = 20, θ = 27°133views
Textbook QuestionFor each pair of vectors u and v with angle θ between them, sketch the resultant.|u| = 20, |v| = 30, θ = 30°165views
Textbook QuestionUse the parallelogram rule to find the magnitude of the resultant force for the two forces shown in each figure. Round answers to the nearest tenth.<IMAGE>134views
Textbook QuestionWrite each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.<IMAGE>130views
Textbook QuestionUse the parallelogram rule to find the magnitude of the resultant force for the two forces shown in each figure. Round answers to the nearest tenth.<IMAGE>292views
Textbook QuestionTwo forces act on a point in the plane. The angle between the two forces is given. Find the magnitude of the resultant force.forces of 250 and 450 newtons, forming an angle of 85°191views
Textbook QuestionTwo forces act on a point in the plane. The angle between the two forces is given. Find the magnitude of the resultant force.forces of 116 and 139 lb, forming an angle of 140° 50′132views
Textbook QuestionTwo tugboats are pulling a disabled speedboat into port with forces of 1240 lb and 1480 lb. The angle between these forces is 28.2°. Find the direction and magnitude of the equilibrant.147views
Textbook QuestionTwo rescue vessels are pulling a broken-down motorboat toward a boathouse with forces of 840 lb and 960 lb. The angle between these forces is 24.5°. Find the direction and magnitude of the equilibrant.162views
Textbook QuestionTwo forces of 692 newtons and 423 newtons act on a point. The resultant force is 786 newtons. Find the angle between the forces.145views
Textbook QuestionTwo forces of 128 lb and 253 lb act on a point. The resultant force is 320 lb. Find the angle between the forces.172views
Textbook QuestionA force of 176 lb makes an angle of 78° 50′ with a second force. The resultant of the two forces makes an angle of 41° 10′ with the first force. Find the magnitudes of the second force and of the resultant.<IMAGE>179views
Textbook QuestionA force of 28.7 lb makes an angle of 42° 10′ with a second force. The resultant of the two forces makes an angle of 32° 40′ with the first force. Find the magnitudes of the second force and of the resultant.<IMAGE>142views
Textbook QuestionA force of 25 lb is required to hold an 80-lb crate on a hill. What angle does the hill make with the horizontal? 165views
Textbook QuestionFind the force required to keep a 3000-lb car parked on a hill that makes an angle of 15° with the horizontal.151views
Textbook QuestionTo build the pyramids in Egypt, it is believed that giant causeways were constructed to transport the building materials to the site. One such causeway is said to have been 3000 ft long, with a slope of about 2.3°. How much force would be required to hold a 60-ton monolith on this causeway?<IMAGE>152views1rank
Textbook QuestionCONCEPT PREVIEW Refer to vectors a through h below. Make a copy or a sketch of each vector, and then draw a sketch to represent each of the following. For example, find a + e by placing a and e so that their initial points coincide. Then use the parallelogram rule to find the resultant, as shown in the figure on the right.<IMAGE>-b125views
Textbook QuestionFind the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary.〈5, 7〉121views
Textbook QuestionA force of 30.0 lb is required to hold an 80.0-lb pressure washer on an incline. What angle does the incline make with the horizontal?147views
Textbook QuestionTwo people are carrying a box. One person exerts a force of 150 lb at an angle of 62.4° with the horizontal. The other person exerts a force of 114 lb at an angle of 54.9°. Find the weight of the box. <IMAGE>170views
Textbook QuestionA crate is supported by two ropes. One rope makes an angle of 46° 20′ with the horizontal and has a tension of 89.6 lb on it. The other rope is horizontal. Find the weight of the crate and the tension in the horizontal rope.143views
Textbook QuestionA ship leaves port on a bearing of 34.0° and travels 10.4 mi. The ship then turns due east and travels 4.6 mi. How far is the ship from port, and what is its bearing from port?170views
Textbook QuestionA luxury liner leaves port on a bearing of 110.0° and travels 8.8 mi. It then turns due west and travels 2.4 mi. How far is the liner from port, and what is its bearing from port?146views
Textbook QuestionStarting at point A, a ship sails 18.5 km on a bearing of 189°, then turns and sails 47.8 km on a bearing of 317°. Find the distance of the ship from point A.271views
Textbook QuestionStarting at point X, a ship sails 15.5 km on a bearing of 200°, then turns and sails 2.4 km on a bearing of 320°. Find the distance of the ship from point X.153views
Textbook QuestionLet u = 〈-2, 1〉, v = 〈3, 4〉, and w = 〈-5, 12〉. Evaluate each expression.(3u) • v126views
Textbook QuestionLet u = 〈-2, 1〉, v = 〈3, 4〉, and w = 〈-5, 12〉. Evaluate each expression.u • v - u • w136views
Textbook QuestionCONCEPT PREVIEW Refer to vectors a through h below. Make a copy or a sketch of each vector, and then draw a sketch to represent each of the following. For example, find a + e by placing a and e so that their initial points coincide. Then use the parallelogram rule to find the resultant, as shown in the figure on the right.<IMAGE>2c117views
Textbook QuestionUse the figure to find each vector: u + v. Use vector notation as in Example 4.<IMAGE> 119views
Textbook QuestionUse the figure to find each vector: u - v. Use vector notation as in Example 4.<IMAGE> 128views
Textbook QuestionUse the figure to find each vector: - v. Use vector notation as in Example 4.<IMAGE> 133views
Textbook QuestionA force of 18.0 lb is required to hold a 60.0-lb stump grinder on an incline. What angle does the incline make with the horizontal?146views
Textbook QuestionOne boat pulls a barge with a force of 100 newtons. Another boat pulls the barge at an angle of 45° to the first force, with a force of 200 newtons. Find the resultant force acting on the barge, to the nearest unit, and the angle between the resultant and the first boat, to the nearest tenth.133views
Textbook QuestionSolve each problem. See Examples 5 and 6.Bearing and Ground Speed of a Plane An airline route from San Francisco to Honolulu is on a bearing of 233.0°. A jet flying at 450 mph on that bearing encounters a wind blowing at 39.0 mph from a direction of 114.0°. Find the resulting bearing and ground speed of the plane.173views
Textbook QuestionA plane flies 650 mph on a bearing of 175.3°. A 25-mph wind, from a direction of 266.6°, blows against the plane. Find the resulting bearing of the plane.135views
Textbook QuestionA pilot is flying at 168 mph. She wants her flight path to be on a bearing of 57° 40′. A wind is blowing from the south at 27.1 mph. Find the bearing she should fly, and find the plane's ground speed.149views
Textbook QuestionA plane is headed due south with an airspeed of 192 mph. A wind from a direction of 78.0° is blowing at 23.0 mph. Find the ground speed and resulting bearing of the plane.135views
Textbook QuestionRefer to vectors a through h below. Make a copy or a sketch of each vector, and then draw a sketch to represent each of the following. For example, find a + e by placing a and e so that their initial points coincide. Then use the parallelogram rule to find the resultant, as shown in the figure on the right.<IMAGE>a + b120views