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

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Questions
1 The area of the quadrilateral ABCD, where A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2) is equal to
A 9 sq. units
B 18 sq. units
C 27 sq. units
D 81 sq. units

Answer:9 sq. units
2 The reflection of the point (a, β, γ) in the xy-plane is
A (α, β, 0)
B (0, 0, γ)
C (- α, – β, γ)
D (α, β, γ)

Answer:(α, β, γ)
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3 The equation of the plane through point (1, 2, -3) which is parallel to the plane 3x- 5y + 2z = 11 is given by
A 3x – 5y + 2z – 13 = 0
B 5x – 3y + 2z + 13 = 0
C 3x – 2y + 5z + 13 = 0
D 3x – 5y + 2z + 13 = 0

Answer:3x – 5y + 2z + 13 = 0
4 The line x = 1, y = 2 is
A parallel to x-axis
B parallel to y-axis
C parallel to z-axis
D None of these

Answer:parallel to z-axis
5 If a line makes angles α, β, γ with the axis then cos 2α + cos 2β + cos 2γ =
A -2
B -1
C 1
D 2

Answer:-1
6 If α, β, γ are the angle which a half ray makes with the positive directions of the axis then sin²α + sin²β + sin²γ =
A 1
B 2
C 0
D -1

Answer:2
7 The plane x + y = 0
A is parallel to z-axis
B is perpendicular to z-axis
C passes through z-axis
D None of these

Answer:passes through z-axis
8 The locus of xy + yz = 0 is
A A pair of st. lines
B A pair of parallel lines
C A pair of parallel planes
D A pair of perpendicular planes

Answer:A pair of perpendicular planes
9 The equation of the plane through the origin and parallel to the plane 3x – 4y + 5z + 6 = 0
A 3x – 4y – 5z – 6 = 0
B 3x – 4y + 5z + 6 = 0
C 3x – 4y + 5z = 0
D 3x + 4y – 5z + 6 = 0

Answer:3x – 4y + 5z = 0
10 The direction ratios of the line of intersection of the planes 3x + 2y – z = 5 and x – y + 2z = 3 are
A 3, 2, -1
B -3, 7, 5
C 1, -1, 2
D – 11, 4, -5

Answer:-3, 7, 5
11 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:7, 4,-2
12 If a line makes angles Q1, Q21 and Q3 respectively with the coordinate axis then the value of cos² Q1 + cos² Q2 + cos² Q3
A 2
B 1
C 4
D 3/2

Answer:1
13 The distance of the point (-3, 4, 5) from the origin
A 50
B 5√2
C 6
D None of these

Answer:5√2
14 The equation x² – x – 2 = 0 in three dimensional space is represented by
A A pair of parallel planes
B A pair of straight lines
C A pair of perpendicular plane
D None of these

Answer:A pair of parallel planes
15 How many lines through the origin in make equal angles with the coordinate axis?
A 1
B 4
C 8
D 2

Answer:8
16 The direction cosines of any normal to the xy plane are
A 1, 0 ,0
B 0, 1, 0
C 1, 1, 0
D 1, 1, 0

Answer:1, 1, 0
17 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 st. line

Answer:two plane are right angles
18 (2, – 3, – 1) 2x – 3y + 6z + 7 = 0
A 4
B 3
C 2
D 1/5

Answer:3
19 If 2x + 5y – 6z + 3 = 0 be 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:2x + 5y – 6z + k = 0
20 The distance of the plane 2x – 3y + 6z + 7 = 0 from the point (2, -3, -1) is
A 4
B 3
C 2
D 1/5

Answer:2

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