Class 11 NCERT Solutions- Chapter 12 Introduction to three dimensional Geometry – Exercise 12.1

Problem 1: A point is on the x-axis. What are its y coordinate and z-coordinates?

Solution:

If a point is on the x-axis, then the coordinates of y and z are 0.

So the point is (x, 0, 0)

Problem 2: A point is in the XZ-plane. What can you say about its y-coordinate?

Solution:

If a point is in XZ plane, 

So its y-coordinate is 0

Problem 3: Name the octants in which the following points lie:

(1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (– 4, 2, –5), (– 4, 2, 5), (–3, –1, 6) (2, – 4, –7).

Solution:

Octants	I	II	III	IV	V	VI	VII	VIII
x	+	–	–	+	+	–	–	+
y	+	+	–	–	+	+	–	–
z	+	+	+	+	–	–	–	–

(i) (1, 2, 3)

Here x is positive, y is positive and z is positive.

So it lies in I octant.

(ii) (4, -2, 3)

Here x is positive, y is negative and z is positive.

So it lies in IV octant.

(iii) (4, -2, -5)

Here x is positive, y is negative and z is negative.

So it lies in VIII octant.

(iv) (4, 2, -5)

Here x is positive, y is positive and z is negative.

So it lies in V octant.

(v) (-4, 2, -5)

Here x is negative, y is positive and z is negative.

So it lies in VI octant.

(vi) (-4, 2, 5)

Here x is negative, y is positive and z is positive.

So it lies in II octant.

(vii) (-3, -1, 6)

Here x is negative, y is negative and z is positive.

So it lies in III octant.

(viii) (2, -4, -7)

Here x is positive, y is negative and z is negative.

So it lies in VIII octant.

Problem 4: Fill in the blanks:

(i) The x-axis and y-axis taken together determine a plane known as _______.

Solution:

The x-axis and y-axis taken together determine a plane known as XY Plane.

(ii) The coordinates of points in the XY-plane are of the form _______.

Solution:

The coordinates of points in the XY-plane are of the form (x, y, 0).

(iii) Coordinate planes divide the space into ______ octants.

Solution:

Coordinate planes divide the space into eight octants.

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