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Free download in PDF Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries./p>
(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)
(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
(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
(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
(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
(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)
(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
(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)
(15)
The maximum distance between points (3sin θ, 0, 0) and (4cos θ, 0, 0) is
(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)
(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)
(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
(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
(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
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