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Class 11 Maths Chapter 11: Introduction to Three Dimensional Geometry MCQs with answers

10 multiple-choice questions on Introduction to Three Dimensional Geometry, each with its answer and the reason, written from the NCERT chapter. For school exams on the CBSE pattern and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1
Which of the following points lies on the y-axis?
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Answer: (a) (0, −4, 0)

A point on the y-axis has the form (0, y, 0): its x and z coordinates are both zero. Only (0, −4, 0) has this form.

Question 2
A point lies in octant IV. The signs of its x, y and z coordinates are, respectively,
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Answer: (c) +, −, +

From Table 11.1, octant IV is XOY′Z: x positive, y negative, z positive, i.e. (+, −, +).

Question 3
The perpendicular distance of the point P(3, −7, 4) from the ZX-plane is
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Answer: (b) 7

The y-coordinate of a point is its perpendicular distance from the ZX-plane, so the distance is |−7| = 7. (3 is the distance from the YZ-plane, 4 from the XY-plane.)

Question 4
The coordinate planes XOY and YOZ intersect along the
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Answer: (d) y-axis

The plane XOY contains the x and y axes and the plane YOZ contains the y and z axes; the line common to both is Y′OY, the y-axis.

Question 5
In how many of the eight octants is the z-coordinate of every point positive?
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Answer: (b) 4

From Table 11.1, z is positive in octants I, II, III and IV and negative in V to VIII: four octants.

Question 6
The octant X′OY′Z is numbered
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Answer: (d) III

The octants XOYZ, X′OYZ, X′OY′Z, XOY′Z, ... are numbered I, II, III, IV, ... in that order, so X′OY′Z is octant III.

Question 7
The foot of the perpendicular drawn from P(4, −3, 6) to the XY-plane is
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Answer: (a) (4, −3, 0)

The foot M of the perpendicular PM on the XY-plane keeps the x and y coordinates of P and has z = 0: M is (4, −3, 0), and MP = 6.

Question 8
A point lies on the x-axis, on the side of OX′, at a distance of 5 units from the origin. Its coordinates are
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Answer: (c) (−5, 0, 0)

A point on the x-axis is (x, 0, 0). Distances measured along OX′, behind the YZ-plane, are negative, so x = −5.

Question 9
If the plane XOY is taken as horizontal, the line Z′OZ is
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Answer: (d) vertical

Z′OZ is perpendicular to the plane XOY; with XOY horizontal, Z′OZ is vertical.

Question 10
According to the chapter's Historical Note, the three coordinate planes we use today were introduced by
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Answer: (b) J. Bernoulli, in a letter to Leibnitz

The Historical Note credits J. Bernoulli (1667-1748), in a letter of 1715 to Leibnitz, with the three coordinate planes; Parent gave the first systematic development of solid analytical geometry, and Euler took it up systematically later.

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