Question

Class 12 Maths MCQ Questions of Three Dimensional Geometry with Answers?

Answer 1

Students are encouraged to solve the Three Dimensional Geometry MCQ Questions of Class 12 to know various ideas. Every one of the ideas of Three Dimensional Geometry of class 12 is significant for Students according to the exam perspective to get more marks.  Practicing the Multiple choice Questions on Three Dimensional Calculation Class 12 with answers will support your certainty consequently assisting you with scoring high in the exam.

Class 12 Maths MCQ Questions of Three Dimensional Geometry with Answers are accessible here to help the understudies who are appearing up for the CBSE board exams. Understudies can refer to all the significant MCQ Questions for various ideas gave at Sarthaks eConnect to better prepare for exams. Explore MCQ Questions for Class 12 Maths with answers furnished with definite solutions.

Practice MCQ Question for Class 12 Maths chapter-wise

1. The distance of point (2, 5, 7) from the x-axis is

(a) 2
(b) \(\sqrt{74}\)
(c) \(\sqrt{29}\)
(d) \(\sqrt{53}\)

2. P is a point on the line segment joining the points (3, 2, -1) and (6, 2, -2). If y -coordinate of point P is 2, then its x-coordinate will be

(a) 2
(b) 1
(c) -1
(d) -2

3. P is a point on the line segment joining the points (3, 5, -1) and (6, 3, -2). If y -coordinate of point P is 2, then its x-coordinate will be

(a) 2
(b) 17/3
(c) 15/2
(d) -5

4. Direction ratios of a line are 2, 3, -6. Then direction cosines of a line making obtuse angle with the y-axis are

(a) 2/7,3/7,-6/7
(b) -2/7,3/7,-6/7
(c) -2/7,-3/7,6/7
(d) -2/7,-3/7,-6/7

5.  A line makes angle α, β, γ with x-axis, y-axis and z-axis respectively then cos 2α + cos 2β + cos 2γ is equal to

(a) 2
(b) 1
(c) -2
(d) -1

6. The equations of y-axis in space are

(a) x = 0, y = 0
(b) x = 0, z = 0
(c) y = 0, z = 0
(d) y = 0.

7. If the direction cosines of a line are k/3,k/3,k/3, then value of k is

(a) k > 0
(b) 0 < k < 1.
(c) k = 1/3
(d) k = ±3

8. The line joining the points (0, 5, 4) and (1, 3, 6) meets XY-plane at the point 

(a) -2, 9, 0 
(b) -2, 9, 0 
(c) -2, 8, 0 
(d) -2, 9, 6

9. A line makes angles π/4,3π/4 with x-axis and y-axis respectively. Then the angle which it makes with z-axis can be _

(a) π, 0
(b) π , π
(c) π , 1
(d) none of these

10. The direction cosines of the y-axis are

(a) (6, 0, 0)
(b) (1, 0, 0)
(c) (0, 1, 0)
(d) (0, 0, 1)

11. In three dimensional space, the equation x²−x−2 = 0 represents

(a) a pair of straight lines
(b) a set containing two distinct points
(c) a pair of parallel planes
(d) none of these

12. The vector equation for the line passing through the points (–1, 0, 2) and (3, 4, 6) is:

(a) i +2k + λ(4i + 4j + 4k)
(b) i –2k + λ(4i + 4j + 4k)
(c) -i+2k+ λ(4i + 4j + 4k)
(d) -i+2k+ λ(4i – 4j – 4k)

13. Number of lines making equal angles with the co-ordinate axes are is 

(a) 1
(b) 4
(c) 8
(d) 2

14. Distance of the point (3, 4, 5) from the origin (0, 0, 0) is

(a) \(\sqrt{50}\)
(b) 3
(c) 4
(d) 5

15. The distance between the planes 2x−3y + 6z+12=0 and 2x−3y+6z−2=0 is

(a) 10/7
(b) 2/7
(c) 2
(d) 24/7

16. 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

17. Which of the following is false?

(a) Addition is commutative in N. 
(b) Multiplication is associative in N.
(c) If a * b =a^b for all a,b ∈ N then * is commutative in N.
(d) Addition is associative in N

18. Which of the following is false?

(a) meet in a unique point
(b) meet in a line
(c) meet taken two at a time in parallel lines
(d) None of these

19. The coordinates of the mid-point of the line segment joining the points (2,3) and (4,7).

(a) (3,5) 
(b) (2,5)
(c) (4,5)
(d) None of these

20. The coordinates of the mid-point of the line segment joining the points (3,4) and (5,6).

(a) (3,5) 
(b) (2,5)
(c) (4,5)
(d) None of these

Answer 2

1. Answer: (b) 

Explanation: \(\sqrt{5^2+7^2}\)

\(=\sqrt{25+49}\)

\(=\sqrt{74}\)

2. Answer: (a) 2

Explanation: Let P divides the line segment in the ratio of λ: 1, x - coordinate of the point P may be expressed as

\(x=\frac{6\lambda+3}{\lambda+1}\) giving \(\frac{6\lambda+3}{\lambda+1}=5\)

so that λ = 2. Thus y-coordinate of P is

\(\frac{2\lambda+2}{\lambda+1}=2\)

3. Answer: (c) 15/2

Explanation: Let P divides the line segment in the ratio of λ: 1, x - coordinate of the point P may be expressed as

\(\therefore=\frac{3k+5}{k+1}=2\)  

 \(\frac{6k+3}{ka+1}=\frac{-18+3}{-3+1}\)

= 15/2

4. Answer: (c) -2/7,-3/7,6/7

Explanation:  As direction cosines of a line whose direction ratio are 2,3, -6 are 2/7,3/7,−6/7.
As angle with the y-axis is obtuse, ∴ cos β < 0, Therefore direction ratios are -2/7,-3/7,6/7.

5. Answer: (d) -1

Explanation: cos²α + cos²β + cos²\(\gamma\)

= 2(cos² + cos²+ cos²\(\gamma\))⁻³

= 2−3

= −1

= (cos²α + cos²β + cos²\(\gamma\)= 1)

6. Answer: (b) x = 0, z = 0

Explanation: As on the y-axis, x-coordinate and z-coordinate are zeroes.

7. Answer: (d) k = ± 3

Explanation: \(3\times\frac{k^2}{9}=1\)  

k = ±3  

8. Answer: (a) -2, 9, 0 

Explanation: (a) -2, 9, 0 as lone in \(\frac{x-1} 1=\frac{y-3}{-2} =\frac{z-6}{2}=\lambda\)

General point on line is (λ + 1, -2λ + 3, 2λ + 6). If it meets AT-plane, then 

2λ + 6 = 0

λ = – 3

∴ Point is (-2, 9, 0)

9. Answer: (a) 

Explanation: 0,π, as \(cos^2\frac{\pi}{4}+cos^2\frac{\pi}{4}+cos^2\gamma=1\)

= 1/2 + 1/2 + \(cos^\gamma=1\)

\(cos\gamma=0\)

\(\gamma=0,\pi\)

10. Answer: (c) (0, 1, 0)

Explanation: The Y-axis makes angles 90°, 0° and 90° with the positive directions of X-axis, Y-axis and Z-axis, respectively, then cos 90° = 0, cos 0° = 1, cos 90° = 0 are the directions cosines of the line.

11. Answer: (c) a pair of parallel planes

Explanation: x² −x −2 = 0

⇔(x−2) (x+1) = 0

x = 2, x= −1 . which are the planes (both parallel to YOZ plane

12. Answer: (c) 

Explanation: The vector equation of the line is given by:

r = a + λ (b – a), λ ∈ R

Let a = -i + 2k

And b = 3i + 4j + 6k

b – a = 4i + 4j + 4k

Let the vector equation be r, then;

r = -i + 2k + λ (4i + 4j + 4k)

13.  Answer: (d) 2

Explanation: There are two different lines that make equal angles with the co-ordinate axes.They are y = x line and y = - x line.

14. Answer: (a) 

Explanation: Let P be the point whose coordinate is (3, 4, 5) and Q represents the origin

\(PQ=\sqrt{(3-0)^2+(4-0)^2+(5-0)^2}\)

\(=\sqrt{9+16+25}\)

\(=\sqrt{50}\)

∴ Distance of the point (3, 4, 5) from the origin (0, 0, 0) is \(\sqrt{50}\)

15. Answer: (c) 

Explanation: The given equations of the plane are 2x − 3y + 6z +12=0 and 2x −3y + 6z + −2 = 0.

\(=\frac{|d_1-d_2|}{\sqrt{a^2+b^2+c^2}}\)

\(=\frac{|12-(-2)}{\sqrt{2^2+3^2+6^2}}\)

= 14/7

= 2.

16. Answer: (d) a pair of perpendicular planes

Explanation: Locus represented by xy+ yz =0

⇒ y(x+z) =0

The planes y=0 and x+z =0 are perpendicular.

17. Answer: (c) 

Explanation: Since, for the set of natural numbers with respect to addition, it is commutative and associative.  Also, for the set of natural numbers with respect to multiplication, it is associative.

18. Answer: (a) meet in a unique point

Explanation: The planes x + y = 0 i.e. x = - y and y + z = 0 i.e. z = -y meet in the line

x/1 = y/−1 = z/1 .

Any point on this line is (t, -t, t). This point lies in the plane x + z = 0 if t + t = 0 ⇒ t = 0 .

So the three planes meet in a unique point (0, 0, 0).

19. Answer: (a) (3,5) 

Explanation: \((\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)

\(=(\frac{2+4}{2},\frac{3+7}{2})\)

\(=(\frac{6}{2},\frac{10}{2})\)

= (3,5).

20. Answer: (c) (4,5)

Explanation: \((\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)

\(=(\frac{3+5}{2},\frac{4+6}{2})\)

\(=(\frac{8}{2},\frac{10}{2})\)

= (4,5)

Click here to practice more MCQ Question for Three Dimensional Geometry Class 12