Exam 11: Section 3: Vectors and the Geometry of Space

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Suppose a 58000-pound truck is parked on a Suppose a 58000-pound truck is parked on a   slope as shown in the figure. Assume the only force to overcome is that due to gravity. Find the force required to keep the truck from rolling down the hill. Round your answer to two decimal places.  slope as shown in the figure. Assume the only force to overcome is that due to gravity. Find the force required to keep the truck from rolling down the hill. Round your answer to two decimal places. Suppose a 58000-pound truck is parked on a   slope as shown in the figure. Assume the only force to overcome is that due to gravity. Find the force required to keep the truck from rolling down the hill. Round your answer to two decimal places.

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Given Given   and   , find the vector component of u orthogonal to v. and Given   and   , find the vector component of u orthogonal to v. , find the vector component of u orthogonal to v.

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An object is pulled 5 feet horizontally across a floor, using a force of 95 pounds. The direction of the force is An object is pulled 5 feet horizontally across a floor, using a force of 95 pounds. The direction of the force is   above the horizontal. Find the work done. Round your answer to two decimal places. above the horizontal. Find the work done. Round your answer to two decimal places.

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Find the angle between the vectors for u and v given below. Find the angle between the vectors for u and v given below.

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Suppose a 48000-pound truck is parked on a Suppose a 48000-pound truck is parked on a   slope as shown in the figure. Assume the only force to overcome is that due to gravity. Find the force perpendicular to the hill. Round your answer to one decimal place.  slope as shown in the figure. Assume the only force to overcome is that due to gravity. Find the force perpendicular to the hill. Round your answer to one decimal place. Suppose a 48000-pound truck is parked on a   slope as shown in the figure. Assume the only force to overcome is that due to gravity. Find the force perpendicular to the hill. Round your answer to one decimal place.

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Determine whether u and v are orthogonal, parallel and pointing in the same direction, parallel and pointing in opposite directions, or neither. Determine whether u and v are orthogonal, parallel and pointing in the same direction, parallel and pointing in opposite directions, or neither.

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Suppose a car is towed using a force of 1300 newtons. The chain used to pull the car makes a Suppose a car is towed using a force of 1300 newtons. The chain used to pull the car makes a   angle with the horizontal. Find the work done in towing the car 4 kilometers. Round your answer to two decimal places. angle with the horizontal. Find the work done in towing the car 4 kilometers. Round your answer to two decimal places.

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Suppose a toy wagon is pulled by exerting a force of 25 pounds on a handle that makes a Suppose a toy wagon is pulled by exerting a force of 25 pounds on a handle that makes a   angle with the horizontal as shown in the figure below. Find the work done in pulling the wagon 50 feet. Round your answer to one decimal place.  angle with the horizontal as shown in the figure below. Find the work done in pulling the wagon 50 feet. Round your answer to one decimal place. Suppose a toy wagon is pulled by exerting a force of 25 pounds on a handle that makes a   angle with the horizontal as shown in the figure below. Find the work done in pulling the wagon 50 feet. Round your answer to one decimal place.

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Given Given   and   , find the projection of u onto v. and Given   and   , find the projection of u onto v. , find the projection of u onto v.

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Find the angle between the vectors for u and v. Find the angle between the vectors for u and v.

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Determine whether u and v are orthogonal, parallel or neither. Determine whether u and v are orthogonal, parallel or neither.

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Find the direction cosines of the vector u given below. Find the direction cosines of the vector u given below.

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Suppose the vector Suppose the vector   gives the numbers of hamburgers, chicken sandwiches, and cheeseburgers, respectively, sold at a fast-food restaurant in one week. The vector   gives the prices (in dollars) per unit for the three food items. Determine the total revenue that the restaurant earned on its three products for that week. Round your answer to two decimal places. gives the numbers of hamburgers, chicken sandwiches, and cheeseburgers, respectively, sold at a fast-food restaurant in one week. The vector Suppose the vector   gives the numbers of hamburgers, chicken sandwiches, and cheeseburgers, respectively, sold at a fast-food restaurant in one week. The vector   gives the prices (in dollars) per unit for the three food items. Determine the total revenue that the restaurant earned on its three products for that week. Round your answer to two decimal places. gives the prices (in dollars) per unit for the three food items. Determine the total revenue that the restaurant earned on its three products for that week. Round your answer to two decimal places.

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Given Given   and   find   . and Given   and   find   . find Given   and   find   . .

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Given Given   and   find   . and Given   and   find   . find Given   and   find   . .

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Find the direction cosines of the vector u given below. Find the direction cosines of the vector u given below.

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Given Given   , find   . , find Given   , find   . .

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Find the direction angles of the vector u given below. Round your answer to one decimal place. Find the direction angles of the vector u given below. Round your answer to one decimal place.

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