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Exercise 12.1 - Chapter 12 Introduction To Three Dimensional Geometry class 11 ncert solutions Maths - SaraNextGen [2024]


Question 1:

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

Answer:

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

Question 2:

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

Answer:

If a point is in the XZ plane, then its y-coordinate is zero.

Question 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)

Answer:

The x-coordinate, y-coordinate, and z-coordinate of point (1, 2, 3) are all positive. Therefore, this point lies in octant I.

The x-coordinate, y-coordinate, and z-coordinate of point (4, –2, 3) are positive, negative, and positive respectively. Therefore, this point lies in octant IV.

The x-coordinate, y-coordinate, and z-coordinate of point (4, –2, –5) are positive, negative, and negative respectively. Therefore, this point lies in octant VIII.

The x-coordinate, y-coordinate, and z-coordinate of point (4, 2, –5) are positive, positive, and negative respectively. Therefore, this point lies in octant V.

The x-coordinate, y-coordinate, and z-coordinate of point (–4, 2, –5) are negative, positive, and negative respectively. Therefore, this point lies in octant VI.

The x-coordinate, y-coordinate, and z-coordinate of point (–4, 2, 5) are negative, positive, and positive respectively. Therefore, this point lies in octant II.

The x-coordinate, y-coordinate, and z-coordinate of point (–3, –1, 6) are negative, negative, and positive respectively. Therefore, this point lies in octant III.

The x-coordinate, y-coordinate, and z-coordinate of point (2, –4, –7) are positive, negative, and negative respectively. Therefore, this point lies in octant VIII.

Question 4:

Fill in the blanks:

Answer:

(i) The x-axis and y-axis taken together determine a plane known as https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/172/4852/NCERT_16-10-08_Khushboo_11_Math_Ex-12.1_4_SU_SNK_html_dbc8229.gif.

(ii) The coordinates of points in the XY-plane are of the formhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/172/4852/NCERT_16-10-08_Khushboo_11_Math_Ex-12.1_4_SU_SNK_html_m16315b7f.gif.

(iii) Coordinate planes divide the space intohttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/172/4852/NCERT_16-10-08_Khushboo_11_Math_Ex-12.1_4_SU_SNK_html_1aaacbd.gif octants.

Also Read : Exercise-12.2-Chapter-12-Introduction-To-Three-Dimensional-Geometry-class-11-ncert-solutions-Maths

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