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

Questions
1 The image of the point P(1, 3, 4) in the plane 2x – y + z = 0 is
A (-3, 5, 2)
B (3, 5, 2)
C (3, -5, 2)
D (3, 5, -2)

Answer:(-3, 5, 2)
2 If the end points of a diagonal of a square are (1, -2, 3) and (2, -3, 5) then the length of the side of square is
A √3 unit
B 2√3 unit
C 3√3 unit
D 4√3 unit

Answer:√3 unit
3 If P(x, y, z) is a point on the line segment joining Q(2, 2, 4) and R(3, 5, 6) such that the projections of OP on the axes are 13/5, 19/5, 26/5 respectively, then P divides QR in the ration
A 1 : 2
B 3 : 2
C 2 : 3
D 1 : 3

Answer:3 : 2
4 The coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the YZ plane is
A (0, 17/2, 13/2)
B (0, -17/2, -13/2)
C (0, 17/2, -13/2)
D None of these

Answer:(0, 17/2, -13/2)
5 If α, β, γ are the angles made by a half ray of a line respectively with positive directions of X-axis Y-axis and Z-axis, then sin² α + sin² β + sin² γ =
A 1
B 0
C -1
D None of these

Answer:None of these
6 The plane 2x – (1 + a)y + 3az = 0 passes through the intersection of the planes
A 2x – y = 0 and y + 3z = 0
B 2x – y = 0 and y – 3z = 0
C 2x + 3z = 0 and y = 0
D 2x – 3z = 0 and y = 0

Answer:2x – 3z = 0 and y = 0
7 The image of the point P(1, 3, 4) in the plane 2x – y + z = 0 is
A (-3, 5, 2)
B (3, 5, 2)
C (3, -5, 2)
D (3, 5, -2)

Answer:(-3, 5, 2)
8 The equation of plane passing through the point i + j + k and parallel to the plane r . (2i – j + 2k) = 5 is
A r . (2i – j + 2k) = 2
B r . (2i – j + 2k) = 3
C r . (2i – j + 2k) = 4
D r . (2i – j + 2k) = 5

Answer:r . (2i – j + 2k) = 3
9 In a three dimensional space, the equation 3x – 4y = 0 represents
A a plane containing Y axis
B none of these
C a plane containing Z axis
D a plane containing X axis

Answer:a plane containing Z axis
10 Three planes x + y = 0, y + z = 0, and x + z = 0
A none of these
B meet in a line
C meet in a unique point
D meet taken two at a time in parallel lines

Answer:meet in a unique point
11 The points on the y- axis which are at a distance of 3 units from the point (2, 3, -1) is
A either (0, -1, 0) or (0, -7, 0)
B either (0, 1, 0) or (0, 7, 0)
C either (0, 1, 0) or (0, -7, 0)
D either (0, -1, 0) or (0, 7, 0)

Answer:either (0, -1, 0) or (0, 7, 0)
12 The cartesian equation of the line is 3x + 1 = 6y – 2 = 1 – z then its direction ratio are
A 1/3, 1/6, 1
B -1/3, 1/6, 1
C 1/3, -1/6, 1
D 1/3, 1/6, -1

Answer:1/3, 1/6, 1
13 The equation of the set of point P, the sum of whose distance from A(4, 0, 0) and B(-4, 0, 0) is equal to 10 is
A 9x² + 25y² + 25z² + 225 = 0
B 9x² + 25y² + 25z² – 225 = 0
C 9x² + 25y² – 25z² – 225 = 0
D 9x² – 25y² – 25z² – 225 = 0

Answer:9x² + 25y² + 25z² – 225 = 0
14 A vector r is equally inclined with the coordinate axes. If the tip of r is in the positive octant and |r| = 6, then r is
A 2√3(i – j + k)
B 2√3(-i + j + k)
C 2√3(i + j – k)
D 2√3(i + j + k)

Answer:2√3(i + j + k)
15 The maximum distance between points (3sin θ, 0, 0) and (4cos θ, 0, 0) is
A 3
B 2
C 4
D 5

Answer:5
16 The coordinate of foot of perpendicular drawn from the point A(1, 0, 3) to the join of the point B(4, 7, 1) and C(3, 5, 3) are
A (5/3, 7/3, 17/3)
B (5, 7, 17)
C (5/3, -7/3, 17/3)
D (5/7, -7/3, -17/3)

Answer:(5/3, 7/3, 17/3)
17 A vector r is equally inclined with the coordinate axes. If the tip of r is in the positive octant and |r| = 6, then r is
A 2√3(i – j + k)
B 2√3(-i + j + k)
C 2√3(i + j – k)
D 2√3(i + j + k)

Answer:2√3(i + j + k)
18 The locus of a point which moves so that the difference of the squares of its distances from two given points is constant, is a
A Straight line
B Plane
C Sphere
D None of these

Answer:Plane
19 The maximum distance between points (3sin θ, 0, 0) and (4cos θ, 0, 0) is
A 3
B 4
C 5
D Can not be find

Answer:5
20 The angle between the vectors with direction ratios are 4, -3, 5 and 3, 4, 5 is
A π/2
B π/3
C π/4
D π/6

Answer:π/3

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