# MCQ Questions Chapter 12 Introduction to Three-Dimensional Geometry Class 11 Mathematics

Please refer to MCQ Questions Chapter 12 Introduction to Three-Dimensional Geometry Class 11 Mathematics with answers provided below. These multiple-choice questions have been developed based on the latest NCERT book for class 11 Mathematics issued for the current academic year. We have provided MCQ Questions for Class 11 Mathematics for all chapters on our website. Students should learn the objective based questions for Chapter 12 Introduction to Three-Dimensional Geometry in Class 11 Mathematics provided below to get more marks in exams.

## Chapter 12 Introduction to Three-Dimensional Geometry MCQ Questions

Please refer to the following Chapter 12 Introduction to Three-Dimensional Geometry MCQ Questions Class 11 Mathematics with solutions for all important topics in the chapter.

MCQ Questions Answers for Chapter 12 Introduction to Three-Dimensional Geometry Class 11 Mathematics

Question. For every point P(x, y, z) on the xy-plane,
(a) x = 0
(b) y = 0
(c) z = 0
(d) None of these

C

Question. If the origin is the centroid of the triangle with vertices A (2a, 2, 6), B (– 4, 3b, –10) and C (8, 14, 2c), then the sum of value of a and c is
(a) 0
(b) 1
(c) 2
(d) 3

A

Question. Perpendicular distance of the point P(3, 5, 6) from y-axis is
(a) √41
(b) 6
(c) 7
(d) None of these

D

Question. A plane is parallel to yz-plane, so it is perpendicular to:
(a) x-axis
(b) y-axis
(c) z-axis
(d) None of these

A

Question. The perpendicular distance of the point P(6, 7, 8) from xy-plane is
(a) 8
(b) 7
(c) 6
(d) None of these

A

Question. Let (3, 4, – 1) and (– 1, 2, 3) be the end points of a diameter of a sphere. Then, the radius of the sphere is equal to
(a) 2 units
(b) 3 units
(c) 6 units
(d) 7 units

B

Question. The point (– 2, – 3, – 4) lies in the
(a) first octant
(b) seventh octant
(c) second octant
(d) eighth octant

B

Question. The point in YZ-plane which is equidistant from three points A(2, 0, 3), B(0, 3, 2) and C(0, 0, 1) is
(a) (0, 3, 1)
(b) (0, 1, 3)
(c) (1, 3, 0)
(d) (3, 1, 0)

B

Question. If the origin is the centroid of a ΔABC having vertices A(a, 1, 3), B(– 2, b, – 5) and C(4, 7, c), then
(a) a = – 2
(b) b = 8
(c) c = – 2
(d) None of these

A

Question. The three vertices of a parallelogram taken in order are (–1, 0), (3, 1) and (2, 2) respectively. The coordinate of the fourth vertex is
(a) (2,1)
(b) (–2,1)
(c) (1,2)
(d) (1,–2)

B

Question. The equation of set points P such that PA2 + PB2 = 2K2, where A and B are the points (3, 4, 5) and (–1, 3, –7), respectively is
(a) K2 – 109
(b) 2K2 – 109
(c) 3K2 – 109
(d) 4K2 – 10

B

Question. What is the shortest distance of the point (1, 2, 3) from x- axis ?
(a) 1
(b) √6
(c) √13
(d) √14

C

Question. The ratio in which the YZ-plane divide the line segment formed by joining the points (–2, 4, 7) and (3, –5, 8) is 2 : m. The value of m is
(a) 2
(b) 3
(c) 4
(d) 1

B

Question. In three dimensional space the path of a point whose distance from the x-axis is 3 times its distance from the yz -plane is:
(a) y2 + z2 = 9x2
(b) x2+ y2 =3z2
(c) x2+ z2 = 3y2
(d) y2 – z2 = 9x2

A

Question. The octant in which the points (– 3, 1, 2) and (– 3, 1, – 2) lies respectively is
(a) second, fourth
(b) sixth, second
(c) fifth, sixth
(d) second, sixth

D

Question. The ratio in which YZ-plane divides the line segment formed by joining the points (– 2, 4, 7) and (3, – 5, 8), is
(a) 2 : 3 (externally)
(b) 2 : 3 (internally)
(c) 1 : 3 (externally)
(d) 1 : 3 (internally)

B

Question. x-axis is the intersection of two planes are
(a) xy and xz
(b) yz and zx
(c) xy and yz
(d) None of these

A

Question. The point equidistant from the four points (0,0, 0), (3/2, 0, 0), (0,5/2, 0) and (0, 0, 7/2) is:
(a) 2/3 , 1/3 , 2/5
(b) 3, 2, 3/5
(c) 3/4 , 5/4 , 7/4
(d) 1/2,0, −1

C

Question. The points (0, 7, 10), (– 1, 6, 6) and (– 4, 9, 6) form
(a) a right angled isosceles triangle
(b) a scalene triangle
(c) a right angled triangle
(d) an equilateral triangle

A

Question. Distance between the points (2, 3, 5) and (4, 3, 1) is a √5. The value of ‘a’ is
(a) 2
(b) 3
(c) 9
(d) 5

A

Question. L is the foot of the perpendicular drawn from a point P(6, 7, 8) on the xy-plane. The coordinates of point L is
(a) (6, 0, 0)
(b) (6, 7, 0)
(c) (6, 0, 8)
(d) None of these

B

ASSERTION – REASON TYPE QUESTIONS

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Question. Assertion : Points (– 4, 6, 10), (2, 4, 6) and (14, 0, – 2) are collinear.
Reason : Point (14, 0, – 2) divides the line segment joining by other two given points in the ratio 3 : 2 internally.

C

Question. Assertion : The distance of a point P(x, y, z) from the origin O(0, 0, 0) is given by

Reason : A point is on the x-axis. Its y-coordinate and z-coordinate are 0 and 0 respectively.

B

Question. Assertion: The coordinates of the point which divides the join of A (2, –1, 4) and B (4, 3, 2) in the ratio 2 : 3 externally is C (–2, –9, 8)
Reason : If P(x1, y1, z1) and Q(x2, y2, z2) be two points, and let R be a point on PQ produced dividing it externally in the ratio m1 : m2. Then the coordinates of R are

A

Question. Assertion : If P (x, y, z) is any point in the space, then x, y and z are perpendicular distances from YZ, ZX and XY-planes, respectively.
Reason : If three planes are drawn parallel to YZ, ZX and XY-planes such that they intersect X, Y and Z-axes at (x, 0, 0), (0, y, 0) and (0, 0, z), then the planes meet in space at a point P(x, y, z).

B

Question. Assertion : The XY-plane divides the line joining the points (– 1, 3, 4) and (2, – 5, 6) externally in the ratio 2 : 3.
Reason : For a point in XY-plane, its z-coordinate should be zero.

A

Question. Assertion : If three vertices of a parallelogram ABCD are A(3, –1, 2), B (1, 2, –4) and C (–1, 1, 2), then the fourth vertex is (1, –2, 8).
Reason : Diagonals of a parallelogram bisect each other and mid-point of AC and BD coincide.

A

Question. Assertion : The distance between the points P(1, – 3, 4) and Q(– 4, 1, 2) is √5 units.

where, P and Q are (x1, y1, z1) and (x2, y2, z2)

D

Question. Assertion : Points (– 2, 3, 5), (1, 2, 3) and (7, 0, – 1) are collinear.
Reason : Three points A, B and C are said to be collinear, if AB + BC = AC (as shown below).