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
Answer: c
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) π/6
(b) π/2
(c) π/4
(d) 0
Answer: d
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)
Answer: c
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
Answer: b
5. The vector equation of
the line passing through the point (2, -3, 5) and parallel to the vector 3i + 4j − 2k is
(a) (2 + 3λ)I + (4λ + 3)j + (5 − λ)k
(b) (9 + 3λ)I + (λ − 3)j + (5 − 2λ)k
(c) (2 + 3λ)I + (4λ − 3)j + (5 − 2λ)k
(d) (7 + λ)I + (4λ + 3)j + (5 − 2λ)k
Answer: c
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)
Answer: d
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
Answer: d
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) r⃗ = a⃗ + λ(b⃗ + a⃗ )
(b) r⃗ = a⃗ + λ(a⃗ − b⃗ )
(c) r⃗ = λa⃗ + (b⃗ − a⃗ )
(d) r⃗ = a⃗ + λ(b⃗ − a⃗ )
Answer: d
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
Answer: c
10. The vector equation of the plane passing through the origin
and the line of intersection of the plane r.a = λ and r.b = µ is
(a) r.(λa –
µb) = 0
(b) r.(λb –
µa) = 0
(c) r.(λa +
µb)= 0
(d) r.(λb +
µa) = 0
Answer: b
11. The vector equation of a
line passing through the two points P(-5, 3, 1) and Q(4, -3, 2) is
(a) (−5 + λ)I + (3 + λ)j + (1 − λ)k
(b) (−5 + λ)I + (3 + 6λ)j + (1 + λ)k
(c) (5 + 7λ)I + (8 + 6λ)j + (3 − 5λ)k
(d) (−5 + 9λ)I + (3 − 6λ)j + (1 + λ)k
Answer: d
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
Answer: a
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
Answer: c
14. The Cartesian equation
of the plane r⃗. (2i + j − k) = 4 is
(a) x + y –
z = -4
(b) 2x + y
– z = 4
(c) x + y +
z = 4
(d) -2x – y
+ z = 4
Answer: b
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
Answer: b
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
Answer: a
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
Answer: d
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
Answer: a
19. A line makes angles α, β and γ with the coordinate axes. If α
+ β = 90°, then γ is equal to
(a) 180°
(b) 90°
(c) 0°
(d) None of
these
Answer: b
20. If α, β and γ are the
angles which a half ray makes with the positive directions of the axes, then
sin² α + sin² β + sin² γ =
(a) -1
(b) 0
(c) 2
(d) 1
Answer: c