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

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Questions
1 The equation of the plane passing through three non- collinear points with position vectors a, b, c is
A r.(b × c + c × a + a × b) = 0
B r.(b × c + c × a + a × b) = [abc]
C r.(a × (b + c)) = [abc]
D r.(a + b + c) = 0

Answer:r.(b × c + c × a + a × b) = [abc]
2 Find the length of perpendicular from the origin to the plane
A 5/13
B 5/√13
C 5/23
D 5/√13

Answer:5/13
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3 Find the vector equation of the plane which is at a distance of 8 units from the origin and which is normal to the vector
A
B
C
D None of these

Answer:
4 The coordinate of the foot of perpendicular drawn from origin to the plane 2x – 3y + 4z – 6 = 0 is
A
B
C (12, -18, 24)
D

Answer:
5 The direction cosines of the unit vector perpendicular to the plane passing through the origin are
A 6/7,3/7,2/7
B 6, 3, 2
C −6/7,3/7,2/7
D -6, 3, 2

Answer:−6/7,3/7,2/7
6 The angle between the lines x = 1, y = 2 and y = -1, z = 0 is
A 90°
B 30°
C 60°
D 0°

Answer:90°
7 The angle between the line 2x = 3y = -z and 6x = -y = -4z is
A 30°
B 45°
C 90°
D 0°

Answer:90°
8 The vector equation of the line through the points A(3, 4, -7) and B(1, -1, 6) is
A
B
C
D

Answer:
9 The equation of the line joining the points (-3, 4, 11) and (1, -2, 7) is
A Class 12 Maths Chapter 11 Three Dimensional Geometry
B
C
D

Answer:
10 The point A(1, 2, 3), B(-1, -2, -1) and C(2, 3, 2) are three vertices of a parallelogram ABCD. Find the equation of CD.
A
B
C
D

Answer:
11 Find the coordinatets of the point where the line through the points (5, 1, 6) and (3, 4, 1) crosses the yz-plane.
A (0,−17/2,13/2)
B (0,17/2,−13/2)
C (10,19/2,13/2)
D (0, 17, 13)

Answer:(0,17/2,−13/2)
12 The coordinates of a point on the line at a distance of 6√12 from the point (1, 2, 3) is
A (56, 43, 111)
B (56/17,43/17,111/17)
C (2, 1, 3)
D (-2, -1, -3)

Answer:(56/17,43/17,111/17)
13 The equation of the straight line passing through the point (a, b, c) and parallel to Z-axis is
A
B
C
D

Answer:
14 The certesian equation of the line l when it passes through the point (x1, y1, z1) and parallel to the vector

Class 12 Maths Chapter 11 Three Dimensional Geometry

A x – x1 = y – y1 = z – z1
B x + x1 = y + y1 = z + z1
C
D

Answer:
15 If l, m and n are the direction cosines of line l, then the equation of the line (l) passing through (x1, y1, z1) is
A
B
C
D None of these

Answer:
16 The equation of line passing through the point (-3, 2, -4) and equally inclined to the axes are
A x – 3 = y + 2 = z – 4
B x + 3 = y – 2 = z + 4
C
D None of these

Answer:x + 3 = y – 2 = z + 4
17 Find the direction cosines of the line joining A(0, 7, 10) and B(-1, 6, 6).
A
B
C
D None of these

Answer:
18 The coordinates of a point P are (3, 12, 4) w.r.t. origin O, then the direction cosines of OP are
A 2, 12 , 14
B 1/4, 1/3, 1/2
C
D 3/13, 12/13, 4/13

Answer:3/13, 12/13, 4/13
19 If a line makes an angle θ1, θ2, θ3 with the axis respectively, then cos 2θ1 + cos 2θ2 + cos 2θ3 =
A -4
B -2
C -3
D -1

Answer:-1
20 A line makes angles α, β and γ with the co-ordinate axes. If α + β = 90°, then γ is equal to
A 0°
B 90°
C 180°
D None of these

Answer:90°

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