Below you will find **MCQ Questions of Chapter 12 Three Dimensional Geometry Class 11 Maths Free PDF Download** that will help you in gaining good marks in the examinations and also cracking competitive exams. These Class 11 MCQ Questions with answers will widen your skills and understand concepts in a better manner.

# MCQ Questions for Class 11 Maths Chapter 12 Three Dimensional Geometry with answers

1. The locus represented by xy + yz = 0 is

(a) A pair of perpendicular lines

(b) A pair of parallel lines

(c) A pair of parallel planes

(d) A pair of perpendicular planes

► (d) A pair of perpendicular planes

2. The locus of a point P which moves such that PA^{2} – PB2 = 2k^{2} where A and B are (3, 4, 5) and (–1, 3, –7) respectively is

(a) 8x + 2y + 24z – 9 + 2k^{2} = 0

(b) 8x + 2y + 24z – 2k^{2} = 0

(c) 8x + 2y + 24z + 9 + 2k^{2}= 0

(d) None of these

► (c) 8x + 2y + 24z + 9 + 2k^{2}= 0

3. The equation of the plane passing through the point (1, – 3, –2) and perpendicular to planes x + 2y + 2z = 5 and 3x + 3y + 2z = 8, is

(a) 2x – 4y + 3z – 8 = 0

(b) 2x – 4y – 3z + 8 = 0

(c) 2x – 4y + 3z + 8 = 0

(d) None of these

► (a) 2x – 4y + 3z – 8 = 0

4. A and B be the points (3, 4, 5) and (-1, -3, -7), respectively, the equation of the set of points P such that PA^{2} + PB^{2} = k^{2}, where k is a constant will

(a) Have a term of k to the power 1 only

(b) Have a term of k to the power 2 only

(c) Have a term of k to the power 1 and another with k to the power 2

(d) Be independent of k

► (b) Have a term of k to the power 2 only

5. The image of the point P(1, 3, 4) in the plane 2x – y + z = 0 is

(a) (-3, 5, 2)

(b) (3, 5, 2)

(c) (3, -5, 2)

(d) (3, 5, -2)

► (a) (-3, 5, 2)

6. The distance of the point (3, 4, 5) from X- axis is

(a) √41

(b) 3

(c) 5

(d) √34

► (a) √41

7. A variable plane passes through a fixed point (1, 2, 3). The locus of the foot of the perpendicular drawn from origin to this plane is

(a) x^{2} + y^{2} + z^{2} – x – 2y – 3z = 0

(b) x^{2} + 2y^{2} + 3z^{2} – x – 2y – 3z = 0

(c) x^{2} + 4y^{2} + 9z^{2} + x + 2y + 3 = 0

(d) x^{2} + y^{2} + z^{2} + x + 2y + 3z = 0

► (a) x^{2} + y^{2} + z^{2} – x – 2y – 3z = 0

8. Let the points A(a, b, c) and B(a', b', c') be at distances r and r' from origin. The line AB passes through origin when

(a) a'/a = b'/b = c'/c

(b) aa' + bb' + cc' = rr'

(c) aa' + bb' + cc' = r2 + r'2

(d) None of these

► (a) a'/a = b'/b = c'/c

9. The equation xy = 0 in three dimensional space represents

(a) a pair of parallel lines

(b) a pair of planes at right angles

(c) a plane

(d) a pair of straight lines

► (b) a pair of planes at right angles

10. The direction ratios of a normal to the plane through (1, 0, 0), (0, 1, 0), which makes an angle of π/4 with the plane x + y = 3 are

(a) (1, √2, 1)

(b) (1, 1, √2)

(c) (1, 1, 2)

(d) (√2, 1, 1)

► (b) (1, 1, √2)

11. Find the points on z-axis which are at a distance √21 from the point (1, 2, 3).

(a) (0, 0, 7), (0, 0, –1)

(b) (2, 7, 0), (–3, 2, 0)

(c) (1, 7, 0), (4, 3, 0)

(d) (0, 0, –7), (0, 0, 1)

► (a) (0, 0, 7), (0, 0, –1)

12. Three vertices of a parallelogram PQRS are P(3, – 1, 2), Q (1, 2, – 4) and R (- 1, 1, 2). Find the coordinates of the fourth vertex.

(a) (1,-2,-8)

(b) (1,-2,8)

(c) (1,2,8)

(d) (-1,-2,8)

► (b) (1,-2,8)

13. The direction cosines of any normal to the XY plane are

(a) < 1 , 1 , 0 >

(b) < 0 , 0 , 1 >

(c) < 1 , 0 , 0 >

(d) < 0 , 1 , 0 >

► (b) < 0 , 0 , 1 >

14. The numbers 3, 4 , 5 can be

(a) direction cosines of a line in space

(b) coordinates of a point on the line y = 4 , z = 0

(c) direction numbers of a line in space

(d) coordinates of a point in the plane x + y – z = 0

► (c) direction numbers of a line in space

15. A(4,7,8) B(2,3,4) , C (-1,-2,1) and D(1,2,5) are vertices of a quadrilateral. The quadrilateral is a

(a) Rhombus

(b) Rectangle

(c) Square

(d) Parallelogram

► (d) Parallelogram

16. The distance of the point (3, 4, 5) from X-axis is:

(a) √41

(b) 7

(c) 2√11

(d) 5√2

► (a) √41

17. The distance of the point (x , y , z) from the XY –plane is

(a) y

(b) x

(c) z

(d) I z I

► (d) I z I

18. The line x = 1 , y = 2 is

(a) parallel to Y – axis

(b) lies in a plane parallel to XY – plane

(c) parallel to Z – axis

(d) parallel to X – axis

► (c) parallel to Z – axis

19. A point moves so that the sum of the squares of its distances from the six faces of a cube given by x = ± 1, y = ± 1, z = ± 1 is 10 units. The locus of the point is

(a) x^{2} + y^{2} + z^{2} = 1

(b) x^{2} + y^{2} + z^{2} = 2

(c) x + y + z = 1

(d) x + y + z = 2

► (b) x^{2} + y^{2} + z^{2} = 2

20. The distances of the point (1, 2, 3) from the coordinate axes are A, B and C respectively. Which option is correct?

(a) 2A^{2}C^{2} = 13B^{2}

(b) A^{2} = 2C^{2}

(c) B^{2 }= 3C^{2}

(d) A^{2} = B^{2} + C^{2}

► (a) 2A^{2}C^{2} = 13B^{2}

21. How many lines through the origin make equal angles with the coordinate axes?

(a) 1

(b) 4

(c) 8

(d) 2

► (d) 2

22. A point R with x-coordinate 1 lies on the line segment joining the points P(-2, 3,5) and Q (7, 0, -1). The coordinates of the point R are

(a) (1,-2,3)

(b) (-1,2,3)

(c) (-1,-2,-3)

(d) (1,2,3)

► (d) (1,2,3)

Hope the given MCQ Questions will help you in cracking exams with good marks. These **Introduction to Three Dimensional Geometry MCQ Questions** will help you in practising more and more questions in less time.