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UPSC NDA I 2015 Mathematics Paper

Question Numbers: 59-60

Directions: For the next two (2) items that follow:

A point P(1, 2, 3) is one vertex of a cuboid formed by the coordinate planes and the planes passing through P and parallel to the coordinate planes.

Question : 60 of 120

Marks: +1, -0

Solution:

Concept:

A plane parallel to the xy-plane has a constant z-coordinate. Its equation is of the form

z = k

, where

k

is a constant.

Explanation:

The given plane is parallel to the xy-plane, which means it does not tilt along the x or y axes.

Therefore, its equation must be

z = k

The plane passes through the point

P(1, 2, 3)

Substituting the coordinates of

P

into

z = k

gives

3 = k

Hence, the equation of the required plane is

z = 3

This matches option C.

Answer:

z = 3

(Option C)

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