MCQs Questions for Class 12 Maths Chapter 11 Three Dimensional Geometry

# MCQs Questions for Class 12 Maths Chapter 11 Three Dimensional Geometry

## MCQs Questions for Class 12 Maths Chapter 11 Three Dimensional Geometry

In this 21st century, Multiple Choice Questions (MCQs) play a major role to prepare for a competitive examination. CBSE board has also brought a major change in its board exam patterns.

In most of the competitive examinations, only MCQ Questions are asked.

In future, if you want to prepare for competitive examination, then you should more focus on the MCQ questions. Thus, let’s solve these MCQs Questions to make our foundation very strong.

In this post, you will find 20 MCQs questions for class 12 maths chapter 11 three dimensional geometry.

## MCQs Questions for Class 12 Maths Chapter 11 Three Dimensional Geometry

1. The direction ratios of the line segment joining the points P (x1, y1, z1) and Q (x2, y2, z2) is given by ____________, ____________ and ____________
(a) x2 + x1, y2 + y1, z2 + z1
(b) x2 x1, y2 + y1, z2 z1
(c) x2 x1, y2 y1, z2 z1
(d) x2 + x1, y2 y1, z2 + z1

2. The angle between the lines passing through the points (4, 7, 8), (2, 3, 4) and (-1, -2, 1), (1, 2, 5) is
(a) Ï€/6
(b) Ï€/2
(c) Ï€/4
(d) 0

3. The direction cosines of the y-axis are
(a) (6, 0, 0)
(b) (1, 0, 0)
(c) (0, 1, 0)
(d) (0, 0, 1)

4. If the four points (0, -1, -1), (-4, 4, 4), (4, 5, 1) and (3, 9, 4) are coplanar, then the equation of the plane containing them is
(a) 5x + 7y + 11z – 4 = 0
(b) 5x – 7y + 11z + 4 = 0
(c) 5x – 7y – 11z – 4 = 0
(d) 5x + 7y – 11z + 4 = 0

5. The vector equation of the line passing through the point (2, -3, 5) and parallel to the vector 3i + 4j2k is
(a) (2 + 3Î»)I + (4Î» + 3)j + (5 − Î»)k
(b) (9 + 3Î»)I + (Î» − 3)j + (5 2Î»)k
(c) (2 + 3Î»)I + (4Î» − 3)j + (5 2Î»)k
(d) (7 + Î»)I + (4Î» + 3)j + (5 2Î»)k

6. The coordinates of the midpoints of the line segment joining the points (2, 3, 4) and (8, -3, 8) are
(a) (10, 0, 12)
(b) (5, 6, 0)
(c) (6, 5, 0)
(d) (5, 0, 6)

7. The equation of the plane passing through the points P(1, 1, 1), Q(3, -1, 2) and R(-3, 5, -4) is
(a) x + 2y = 0
(b) x – y = 2
(c) -x + 2y = 2
(d) x + y = 2

8. If a line is passing through the two points A(x1, y1, z1) and B(x2, y2, z2), then which of the following is the vector equation of the line?
(a) r
= a + Î»(b + a )
(b) r
= a + Î»(a − b )
(c) r
= Î»a + (b − a )
(d) r
= a + Î»(b − a )

9. If 2x + 5y – 6z + 3 = 0 is the equation of the plane, then the equation of any plane parallel to the given plane is
(a) 3x + 5y – 6z + 3 = 0
(b) 2x – 5y – 6z + 3 = 0
(c) 2x + 5y – 6z + k = 0
(d) None of these

10. The vector equation of the plane passing through the origin and the line of intersection of the plane r.a = Î» and r.b = Âµ is
(a) r.(Î»a – Âµb) = 0
(b) r.(Î»b – Âµa) = 0
(c) r.(Î»a + Âµb)= 0
(d) r.(Î»b + Âµa) = 0

11. The vector equation of a line passing through the two points P(-5, 3, 1) and Q(4, -3, 2) is
(a) (−5 + Î»)I + (3 + Î»)j + (1 − Î»)k
(b) (−5 + Î»)I + (3 + 6Î»)j + (1 + Î»)k
(c) (5 + 7Î»)I + (8 + 6Î»)j + (3 5Î»)k
(d) (−5 + 9Î»)I + (3 6Î»)j + (1 + Î»)k

12. The length of the perpendicular from the point (0, –1, 3) to the plane 2x + y – 2z + 1 = 0 is
(a) 2
(b) 2√3
(c) 3
(d) 0

13. The equation of the plane through the point P(0, -4, -6) and Q(-2, 9, 3) and perpendicular to the plane x – 4y – 2z = 8 is
(a) 3x + 3y – 2z = 0
(b) x – 2y + z = 2
(c) 2x + y – z = 2
(d) 5x – 3y + 2z = 0

14. The Cartesian equation of the plane r. (2i + jk) = 4 is
(a) x + y – z = -4
(b) 2x + y – z = 4
(c) x + y + z = 4
(d) -2x – y + z = 4

15. The equation xy = 0 in three dimensional space is represented by
(a) a plane
(b) two plane are right angles
(c) a pair of parallel planes
(d) a pair of straight line

16. The angle between the planes r(i +2j + k) = 4 and r.(−i + j + 2k) = 9 is
(a) 60°
(b) 30°
(c) 45°
(d) None of these

17. The angle between 2x + 3y – 2z + 4 = 0 and (2, 1, 1) is
(a) 38.2
(b) 19.64
(c) 89.21
(d) 29.34

18. The direction ratios of the normal to the plane 7x + 4y – 2z + 5 = 0 are
(a) 7, 4, -2
(b)7, 4, 5
(c) 7, 4, 2
(d) 4, -2, 5

19. A line makes angles Î±, Î² and Î³ with the coordinate axes. If Î± + Î² = 90°, then Î³ is equal to
(a) 180°
(b) 90°
(c) 0°
(d) None of these