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

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

1. If the line joining the origin and the point (–2, 1, 2) makes angle θ_{1} ,θ_{2} and θ_{3} with the positive direction of the coordinate axes, then the value of cos 2θ_{1} + cos 2θ_{2} + cos 2θ_{3} is

(a) –1

(b) 1

(c) 2

(d) –2

► (a) –1

2. Direction cosines of a line are

(a) The tangents of the angles made by the line with the negative directions of the coordinate axes.

(b) The sines of the angles made by the line with the positive directions of the coordinate axes.

(c) The cotangents of the angles made by the line with the negative directions of the coordinate axes.

(d) The cosines of the angles made by the line with the positive directions of the coordinate axes.

► (d) The cosines of the angles made by the line with the positive directions of the coordinate axes.

3. If l, m, n are the direction cosines of a line, then

(a) l^{2}+ m^{2}+ 2n^{2} = 1.

(b) l^{2}+ 2m^{2}+ n^{2} = 1.

(c) 2l^{2}+ m^{2}+ n^{2} = 1.

(d) l^{2}+ m^{2}+ n^{2} = 1.

► (d) l^{2}+ m^{2}+ n^{2} = 1.

4. Find the distance of the point (0, 0, 0) from the plane 3x – 4y + 12 z = 3

(a) 9/13

(b) 7/13

(c) 5/13

(d) 3/13

► (d) 3/13

5. If l, m and n are the direction cosines of a line, Direction ratios of the line are the numbers which are

(a) Proportional to the direction cosine l of the line

(b) Inversely Proportional to the direction cosines of the line

(c) Inversely Proportional to the direction cosine l of the line

(d) Proportional to the direction cosines of the line.

► (d) Proportional to the direction cosines of the line.

6. The co-ordinates of the point where the line joining the points (2, –3, 1), (3, –4, –5) cuts the plane 2x + y + z = 7 are

(a) (2,1,0)

(b) (3,2,5)

(c) (1,–2,7)

(d) None of these

► (c) (1,–2,7)

7. The length of the perpendicular from the origin to the plane 2x – 3y + 6z = 21 is:

(a) 14 unit

(b) 21 unit

(c) 7 unit

(d) 3 unit

► (d) 3 unit

8. The two lines x = ay + b, z = cy + d and = a' y + b', z = c' y + d' will be perpendicular, iff

(a) aa' + bb' + cc' + 1 = 0

(b) aa' + bb' + cc' = 0

(c) (a + a') (b + b') + (c + c') = 0

(d) aa' + cc' + 1 = 0

► (d) aa' + cc' + 1 = 0

9. Find the distance of the point (3, – 2, 1) from the plane 2x – y + 2z + 3 = 0

(a) 17/3

(b) 19/3

(c) 13/3

(d) 15/3

► (c) 13/3

10. The equation of the plane passing through the line of intersection of the planes x-2y+3z+8=0 and 2x-7y+4z-3=0 and the point (3, 1, -2) is:

(a) 6x-15y+12z+29=0

(b) 6x-15y+16z+29=0

(c) 6x-15y+12z+32=0

(d) 2x-5y+4z+9=0

► (b) 6x-15y+16z+29=0

11. The equation of the plane passing through the points (2, 1, 0), (3, – 2, – 2) and (3, 1, 7) is:

(a) 7x + 3y – z = 17

(b) 7x + 3y – 2z = 21

(c) 7x + 3y – z = 21

(d) -7x – 3y + z = 17

► (a) 7x + 3y – z = 17

12. Determine the direction cosines of the normal to the plane and the distance from the origin. Plane z = 2

(a) 0, 1, 0; 2

(b) 1, 0, 0; 3

(c) 1, 0, 1; 3

(d) 0, 0, 1; 2

► (d) 0, 0, 1; 2

13. The angle between two lines whose direction ratios are 1,2,1 and 2,-3,4 is:

(a) 30°

(b) 60°

(c) 90°

(d) 45°

► (c) 90°

14. Skew lines are lines in different planes which are

(a) intersecting

(b) parallel and intersecting

(c) neither parallel nor intersecting

(d) parallel

► (c) neither parallel nor intersecting

15. The Cartesian form of the equation of the plane is:

(a) 2x+3y-z=10

(b) 2x+3y-z= √14

(c) 2x+3y-z+√14=0

(d) 2x+3y-z+10=0

► (a) 2x+3y-z=10

16. In the following case, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them. 4x + 8y + z – 8 = 0 and y + z – 4 = 0

(a) 45°

(b) 49°

(c) 47°

(d) 43°

► (a) 45°

17. The equation of plane through the intersection of planes (x+y+z =1) and (2x +3y – z+4) =0 is

(a) x(1 + 2k) + y(1 + 3k) + z(1 – k) + (-1 + 4k) = 0

(b) x(1+2k)+y(1-3k)+z(1-k)+(-1+4k) = 0

(c) x(1+2k) +y(1+3k)+z(1-k) +(-1 – 4k) = 0

(d) x (1-2k) + y(1+3k) +z(1-k) +(-1+4k) = 0

► (a) x(1 + 2k) + y(1 + 3k) + z(1 – k) + (-1 + 4k) = 0

18. In the following case, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them. 2x – 2y + 4z + 5 = 0 and 3x – 3y + 6z – 1 = 0

(a) The planes are perpendicular

(b) The planes are parallel

(c) The planes are at 45°

(d) The planes are at 55°

► (b) The planes are parallel

19. The length of the perpendicular from the origin to the plane 3x + 2y – 6z = 21 is:

(a) 3

(b) 14

(c) 21

(d) 7

► (a) 3

20. Find the distance of the point (2, 3, – 5) from the plane x + 2y – 2z = 9

(a) 4

(b) 2

(c) 3

(d) 5

► (c) 3

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