NCERT Solutions for class 12 Maths | Chapter 11 - Three Dimensional Geometry

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Questions
1 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:(5, 0, 6)t
2 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:(0, 1, 0)
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3 The direction ratios of a line are 1,3,5 then its direction cosines are
A 1/√35, 3/√35, 5/√35
B 1/9, 1/3, 5/9
C 5/√35, 3/√35, 1/√35
D None of these

Answer:1/√35, 3/√35, 5/√35
4 The points A (1, 1, 0), B(0, 1, 1), C(1, 0, 1) and D(2/3, 2/3, 2/3)
A Coplanar
B Non-coplanar
C Vertices of a parallelogram
D None of these

Answer:Coplanar
5 The distance of the plane Class 12 Maths Chapter 11 Three Dimensional Geometry from the orgin is
A 1
B 7
C 1/7
D None of these

Answer:1
6 The cosines of the angle between any two diagonals of a cube is
A 1/3
B 1/2
C 2/3
D 1√3

Answer:1/3
7 The planes Class 12 Maths Chapter 11 Three Dimensional Geometry and Class 12 Maths Chapter 11 Three Dimensional Geometry
A parallel
B at right angles
C equidistant front origin
D None of these

Answer:parallel
8 The sine of the angle between the straight line Class 12 Maths Chapter 11 Three Dimensional Geometry and the plane 2x – 2y + z = 5 is
A
B
C
D

Answer:
9 The plane 2x – 3y + 6z – 11 = 0 makes an angle sin-1 (α) with .e-axis. The value of a is equal to
A √3/2
B √2/3
C 2/7
D 3/7

Answer:2/7
10 The distance of the points (2, 1, -1) from the plane x- 2y + 4z – 9 is
A √31/21
B 13/21
C 13/√21
D √π/2

Answer:13/21
11 The direction cosines of the line joining (1, -1, 1) and (-1, 1, 1) are
A 2, -2, 0
B 1, -1, 0
C 1/√2, – 1/√2
D None of these

Answer:1/√2, – 1/√2
12 The length of the ⊥er from the point (0, – 1, 3) to the plane 2x + y – 2z + 1 = 0 is
A 0
B 2√3
C 2/3
D 2

Answer:2
13 If the directions cosines of a line are A, k, k, then
A k > 0
B 0 < k < 1
C k = 1
D Class 12 Maths Chapter 11 Three Dimensional Geometry

Answer:Class 12 Maths Chapter 11 Three Dimensional Geometry
14 Distance of the point (a, β, γ) from y-axis is
A β
B |β|
C 60 J
D

Answer:
15 If the planes a1x + b, y + c, z + d1 = 0 and a2x + b, y + c2z + d2 = 0 are perpendicular to each other then
A
B
C a1a2 + b1b2 + c1c2 = 0
D

Answer:a1a2 + b1b2 + c1c2 = 0
16 The direction ratios of the line joining the points (x, y, z) and (x2, y2, z1) are
A x1 + x2, y1 + y2, z1 + z2
B
C
D x2 – x1, y2 – y1, z2 – z1

Answer:x2 – x1, y2 – y1, z2 – z1
17 The direction cosines of the normal to the plane 2x – 3y – 6z – 3 = 0 are
A 2/7, −3/7, −6/7
B 2/7, 3/7, 6/7
C −2/7, −3/7, −6/7
D None of these

Answer:2/7, −3/7, −6/7
18 The shortest distance between the lines
A 0
B
C
D

Answer:0
19 The lines of intersection of the planes is parallel to the vector
A
B
C
D

Answer:
20 The angle between the planes 2x – y + z = 6 and x + y + 2z = 7 is
A π/4
B π/6
C π/3
D π/2

Answer:π/3

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