Three Dimensional Geometry- Case Based Type Questions- 2 - Free Questions
MCQ Practice Test & Solutions: Test: Three Dimensional Geometry- Case Based Type Questions- 2 (15 Questions)
You can prepare effectively for JEE Mathematics (Maths) Class 12 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Three Dimensional Geometry- Case Based Type Questions- 2". These 15 questions have been designed by the experts with the latest curriculum of JEE 2026, to help you master the concept.
Test Highlights:
- - Format: Multiple Choice Questions (MCQ)
- - Duration: 40 minutes
- - Number of Questions: 15
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Direction: Read the following text and answer the following questions on the basis of the same:
P1 : x + 3y – z = 0 and P2 : y + 2z = 0 are two intersecting planes. P3 is a plane passing through the point (2, 1, –1) and through the line of intersection of P1 and P2.
Q. ______ is a point on P3.
Detailed Solution: Question 1
Direction: Read the following text and answer the following questions on the basis of the same:
P1 : x + 3y – z = 0 and P2 : y + 2z = 0 are two intersecting planes. P3 is a plane passing through the point (2, 1, –1) and through the line of intersection of P1 and P2.
Q. Equation of P3 is _______.
Detailed Solution: Question 2
Direction: Read the following text and answer the following questions on the basis of the same:
P1 : x + 3y – z = 0 and P2 : y + 2z = 0 are two intersecting planes. P3 is a plane passing through the point (2, 1, –1) and through the line of intersection of P1 and P2.
Q. The angle between P1 and P2 is _______.
Detailed Solution: Question 3
Direction: Read the following text and answer the following questions on the basis of the same:
P1 : x + 3y – z = 0 and P2 : y + 2z = 0 are two intersecting planes. P3 is a plane passing through the point (2, 1, –1) and through the line of intersection of P1 and P2.
Q. Equation of plane parallel to P3 and passing through (1, 2, 3) is _______.
Detailed Solution: Question 4
Direction: Read the following text and answer the following questions on the basis of the same:
P1 : x + 3y – z = 0 and P2 : y + 2z = 0 are two intersecting planes. P3 is a plane passing through the point (2, 1, –1) and through the line of intersection of P1 and P2.
Q. Distance of P3 from origin is _______ units.
Detailed Solution: Question 5
Direction: Read the following text and answer the following questions on the basis of the same:
A mobile tower stands at the top of a hill. Consider the surface on which the tower stands as a plane having points A(1, 0, 2), B(3, –1, 1) and C(1, 2, 1) on it. The mobile tower is tied with 3 cables from the points A, B and C such that it stands vertically on the ground. The top of the tower is at the point (2, 3, 1) as shown in the figure.
Q. The coordinates of the foot of the perpendicular drawn from the top of the tower to the ground are
Direction: Read the following text and answer the following questions on the basis of the same:
A mobile tower stands at the top of a hill. Consider the surface on which the tower stands as a plane having points A(1, 0, 2), B(3, –1, 1) and C(1, 2, 1) on it. The mobile tower is tied with 3 cables from the points A, B and C such that it stands vertically on the ground. The top of the tower is at the point (2, 3, 1) as shown in the figure.
Q. The height of the tower from the ground is
Direction: Read the following text and answer the following questions on the basis of the same:
A mobile tower stands at the top of a hill. Consider the surface on which the tower stands as a plane having points A(1, 0, 2), B(3, –1, 1) and C(1, 2, 1) on it. The mobile tower is tied with 3 cables from the points A, B and C such that it stands vertically on the ground. The top of the tower is at the point (2, 3, 1) as shown in the figure.
Q. The equation of the plane passing through the points A, B and C is
Detailed Solution: Question 8
Direction: Read the following text and answer the following questions on the basis of the same:
A mobile tower stands at the top of a hill. Consider the surface on which the tower stands as a plane having points A(1, 0, 2), B(3, –1, 1) and C(1, 2, 1) on it. The mobile tower is tied with 3 cables from the points A, B and C such that it stands vertically on the ground. The top of the tower is at the point (2, 3, 1) as shown in the figure.
Q. The equation of the perpendicular line drawn from the top of the tower to the ground is
Detailed Solution: Question 9
Direction: Read the following text and answer the following questions on the basis of the same:
A mobile tower stands at the top of a hill. Consider the surface on which the tower stands as a plane having points A(1, 0, 2), B(3, –1, 1) and C(1, 2, 1) on it. The mobile tower is tied with 3 cables from the points A, B and C such that it stands vertically on the ground. The top of the tower is at the point (2, 3, 1) as shown in the figure.
Q. The area of ΔABC is
Direction: Read the following text and answer the following questions on the basis of the same:
Consider the plane π1 : 2x – 3y + 4z + 9 = 0 and the point P(1, –2, 3). π1 is a plane parallel to π1 and containing the point P.
Q. The co-ordinates of A are _______.
Detailed Solution: Question 11
Direction: Read the following text and answer the following questions on the basis of the same:
Consider the plane π1 : 2x – 3y + 4z + 9 = 0 and the point P(1, –2, 3). π1 is a plane parallel to π1 and containing the point P.
Q. Distance between π1 and π2 is _______ units.
Detailed Solution: Question 12
Direction: Read the following text and answer the following questions on the basis of the same:
Consider the plane π1 : 2x – 3y + 4z + 9 = 0 and the point P(1, –2, 3). π1 is a plane parallel to π1 and containing the point P.
Q. Equation of π2 is _______.
Detailed Solution: Question 13
Direction: Read the following text and answer the following questions on the basis of the same:
Consider the plane π1 : 2x – 3y + 4z + 9 = 0 and the point P(1, –2, 3). π1 is a plane parallel to π1 and containing the point P.
Q. A is the foot of perpendicular from π to π1. Equation of PA is _______.
Detailed Solution: Question 14
Direction: Read the following text and answer the following questions on the basis of the same:
Consider the plane π1 : 2x – 3y + 4z + 9 = 0 and the point P(1, –2, 3). π1 is a plane parallel to π1 and containing the point P.
Q. The image of π on π1 is _______.
Detailed Solution: Question 15
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