Test: Three Dimensional Geometry- Case Based Type Questions- 1 - JEE MCQ

Direction: Read the following text and answer the following questions on the basis of the same:

Suppose the floor of a hotel is made up of mirror polished Salvatore stone. There is a large crystal chandelier attached to the ceiling of the hotel room. Consider the floor of the hotel room as a plane having the equation x – y + z = 4 and the crystal chandelier is suspended at the point (1, 0, 1).

Q. The equation of the perpendicular from the point (1, 0, 1) to the plane x – y + z = 4 is

Direction: Read the following text and answer the following questions on the basis of the same:

Suppose the floor of a hotel is made up of mirror polished Salvatore stone. There is a large crystal chandelier attached to the ceiling of the hotel room. Consider the floor of the hotel room as a plane having the equation x – y + z = 4 and the crystal chandelier is suspended at the point (1, 0, 1).

Q. The direction cosine of the normal to the plane x – y + z = 4 is

Direction: Read the following text and answer the following questions on the basis of the same:

The Indian coast guard, while patrolling, saw a suspicious boat with people. They were nowhere looking like fishermen. The coast guard were closely observing the movement of the boat for an opportunity to seize the boat. They observed that the boat is moving along a planar surface. At an instant of time, the coordinates of the position of the coast guard helicopter and the boat is (1, 3, 5) and (2, 5, 3) respectively.

Q. At that given instant of time, the equation of line passing through the positions of the helicopter and boat is

Direction: Read the following text and answer the following questions on the basis of the same:

The Indian coast guard, while patrolling, saw a suspicious boat with people. They were nowhere looking like fishermen. The coast guard were closely observing the movement of the boat for an opportunity to seize the boat. They observed that the boat is moving along a planar surface. At an instant of time, the coordinates of the position of the coast guard helicopter and the boat is (1, 3, 5) and (2, 5, 3) respectively.

Q. If the coast guard decide to shoot the boat at that given instant of time, then what is the distance (in meters) that the bullet has to travel?

Direction: Read the following text and answer the following questions on the basis of the same:

The Indian coast guard, while patrolling, saw a suspicious boat with people. They were nowhere looking like fishermen. The coast guard were closely observing the movement of the boat for an opportunity to seize the boat. They observed that the boat is moving along a planar surface. At an instant of time, the coordinates of the position of the coast guard helicopter and the boat is (1, 3, 5) and (2, 5, 3) respectively.

Q. If the line joining the positions of the helicopter and the boat is perpendicular to the plane in which the boat moves, then the equation of the plane is

Direction: Read the following text and answer the following questions on the basis of the same:

The Indian coast guard, while patrolling, saw a suspicious boat with people. They were nowhere looking like fishermen. The coast guard were closely observing the movement of the boat for an opportunity to seize the boat. They observed that the boat is moving along a planar surface. At an instant of time, the coordinates of the position of the coast guard helicopter and the boat is (1, 3, 5) and (2, 5, 3) respectively.

Q. If the coast guard decides to shoot the boat at that given instant of time, when the speed of bullet is 36 m/sec, then what is the time taken for the bullet to travel and hit the boat?

Direction: Read the following text and answer the following questions on the basis of the same:

The Indian coast guard, while patrolling, saw a suspicious boat with people. They were nowhere looking like fishermen. The coast guard were closely observing the movement of the boat for an opportunity to seize the boat. They observed that the boat is moving along a planar surface. At an instant of time, the coordinates of the position of the coast guard helicopter and the boat is (1, 3, 5) and (2, 5, 3) respectively.

Q. At a different instant of time, the boat moves to a different position along the planar surface. What should be the coordinates of the location of the boat if the coast guard shoots the bullet along the line whose equation is x/1 = y-1/2 = z-2/1 for the

bullet to hit the boat?

Direction: Read the following text and answer the following questions on the basis of the same:

A cricket match is organized between two Clubs A and B for which a team from each club is chosen. Remaining players of Club A and Club B are respectively sitting on the plane represented by the equation to cheer the team of their own clubs.

Q. Which of the following is a player of Club B?

Direction: Read the following text and answer the following questions on the basis of the same:

A cricket match is organized between two Clubs A and B for which a team from each club is chosen. Remaining players of Club A and Club B are respectively sitting on the plane represented by the equation to cheer the team of their own clubs.

Q. The magnitude of the normal to the plane on which players of club B are seated, is

Direction: Read the following text and answer the following questions on the basis of the same:

A cricket match is organized between two Clubs A and B for which a team from each club is chosen. Remaining players of Club A and Club B are respectively sitting on the plane represented by the equation to cheer the team of their own clubs.

Q. The Cartesian equation of the plane on which players of Club A are seated is

Direction: Read the following text and answer the following questions on the basis of the same:

A cricket match is organized between two Clubs A and B for which a team from each club is chosen. Remaining players of Club A and Club B are respectively sitting on the plane represented by the equation to cheer the team of their own clubs.

Q. The intercept form of the equation of the plane on which players of Club B are seated is

Direction: Read the following text and answer the following questions on the basis of the same:

A cricket match is organized between two Clubs A and B for which a team from each club is chosen. Remaining players of Club A and Club B are respectively sitting on the plane represented by the equation to cheer the team of their own clubs.

Q. The distance of the plane, on which players of Club B are seated, from the origin is

Direction: Read the following text and answer the following questions on the basis of the same:

The equation of motion of a missile are x = 3t, y = –4t, z = t, where the time ‘t’ is given in seconds, and the distance is measured in kilometres.

Q. At a certain instant of time, if the missile is above the sea level, where the equation of the surface of sea is given by 2x + y + 3z = 1 and the position of the missile at that instant of time is (1, 1, 2), then the image of the position of the rocket in the sea is

Direction: Read the following text and answer the following questions on the basis of the same:

The equation of motion of a missile are x = 3t, y = –4t, z = t, where the time ‘t’ is given in seconds, and the distance is measured in kilometres.

Q. At what distance will the rocket be from the starting point (0, 0, 0) in 5 seconds?

Direction: Read the following text and answer the following questions on the basis of the same:

The equation of motion of a missile are x = 3t, y = –4t, z = t, where the time ‘t’ is given in seconds, and the distance is measured in kilometres.

Q. What is the path of the missile?

Direction: Read the following text and answer the following questions on the basis of the same:

The equation of motion of a missile are x = 3t, y = –4t, z = t, where the time ‘t’ is given in seconds, and the distance is measured in kilometres.

Q. If the position of rocket at a certain instant of time is (5, –8, 10), then what will be the height of the rocket from the ground? (The ground is considered as the xy-plane).

Direction: Read the following text and answer the following questions on the basis of the same:

The equation of motion of a missile are x = 3t, y = –4t, z = t, where the time ‘t’ is given in seconds, and the distance is measured in kilometres.

Q. Which of the following points lie on the path of the missile?