Check the below NCERT MCQ Questions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry with Answers Pdf free download. MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. We have provided Introduction to Three Dimensional Geometry Class 11 Maths MCQs Questions with Answers to help students understand the concept very well.

## Q.1 The ratio in which the line joining the points(1, 2, 3) and (-3, 4, -5) is divided by the xy-plane is

(a) 2 : 5

(b) 3 : 5

(c) 5 : 2

(d) 5 : 3

(b) 3 : 5

## Q.2 The vector equation of a sphere having centre at origin and radius 5 is

(a) |r| = 5

(b) |r| = 25

(c) |r| = √5

(d) none of these

(a) |r| = 5

## Q.3 The distance of the point P(a, b, c) from the x-axis is

(a) √(a² + c²)

(b) √(a² + b²)

(c) √(b² + c²)

(d) None of these

(c) √(b² + c²)

## Q.4 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)

(a) (-3, 5, 2)

## Q.5 The locus of a first-degree equation in x, y, z is a

(a) sphere

(b) straight line

(c) plane

(d) none of these

(c) plane

## Q.6 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

(c) a plane containing Z axis

## Q.7 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

(b) 3 : 2

## Q.8 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

(d) None of these

## Q.9 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)

(d) either (0, -1, 0) or (0, 7, 0)

## Q.10 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)

(a) (-3, 5, 2)

## Q.11 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

(c) 5

## Q.12 Under what condition does the equation x² + y² + z² + 2ux + 2vy + 2wz + d represent a real sphere

(a) u² + v² + w² = d²

(b) u² + v² + w² > d

(c) u² + v² + w² < d

(d) u² + v² + w² < d²

(b) u² + v² + w² > d

## Q.13 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

(a) 1/3, 1/6, 1

## Q.14 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

(b) r . (2i – j + 2k) = 3

## Q.15 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)

(d) 2√3(i + j + k)

## Q.16 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

(b) π/3

## Q.17 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

(c) (0, 17/2, -13/2)

## Q.18 There is one and only one sphere through

(a) 4 points not in the same plane

(b) 4 points not lie in the same straight line

(c) none of these

(d) 3 points not lie in the same line

(a) 4 points not in the same plane

## Q.19 If P is a point in space such that OP = 12 and OP inclined at angles 45 and 60 degrees with OX and OY respectively, then the position vector of P is

(a) 6i + 6j ± 6√2k

(b) 6i + 6√2j ± 6k

(c) 6√2i + 6j ± 6k

(d) None of these

(c) 6√2i + 6j ± 6k

## Q.20 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

(b) 9x² + 25y² + 25z² – 225 = 0

## Class 11 Maths with Answers Chapter Wise

**Chapter 1: Sets Class 11 MCQ Questions****Chapter 2: Relations and Functions Class 11 MCQ Questions****Chapter 3: Trigonometric Functions Class 11 MCQ Questions****Chapter 4: Principle of Mathematical Induction Class 11 MCQ Questions****Chapter 5: Complex Numbers and Quadratic Equations Class 11 MCQ Questions****Chapter 6: Linear Inequalities Class 11 MCQ Questions****Chapter 7: Permutations and Combinations Class 11 MCQ Questions****Chapter 8: Binomial Theorem Class 11 MCQ Questions****Chapter 9: Sequences and Series Class 11 MCQ Questions****Chapter 10: Straight Lines Class 11 MCQ Questions****Chapter 11: Conic Sections Class 11 MCQ Questions****Chapter 12: Introduction to Three Dimensional Geometry Class 11 MCQ Questions****Chapter 13: Limits and Derivatives Class 11 MCQ Questions****Chapter 14: Mathematical Reasoning Class 11 MCQ Questions****Chapter 15: Statistics Class 11 MCQ Questions****Chapter 16: Probability Class 11 MCQ Questions**

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