NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry त्रिविमीय ज्यामिति का परिचय, Free download in PDF for all the students following **NCERT Books** for their study. Applicable for CBSE as well as UP Board students from 2018-19 onward as their are following **CBSE Curriculum 2018-2019**.

## NCERT Solutions for Class 11 Maths Chapter 12

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### Class 11 Maths Chapter 12 Introduction to 3-D Geometry Sols

**Download Exercise 12.1****Download Exercise 12.2****Download Exercise 12.3****Download Miscellaneous Exercise 12****NCERT Books for Class 11****Revision Books for Class 11**- Hindi Medium Solutions will be uploaded very soon.

#### Important Terms of 3-D Geometry

- Three mutually perpendicular lines in space define three mutually perpendicular planes, called
*Coordinate planes*, which in turn divide the space into eight parts known as octants and the lines are known as*Coordinate axes*. - Coordinates of a points lying on x-axis, y-axis & z-axis are of the from (x, 0, 0), (0, y, 0), (0, 0, z) respectively.
- Coordinates of a points lying on xy – plane, yz – plane, and xz – plane are of the from (x, y, 0), (0, y, z), (x, 0, z) respectively.
- The reflection of the point (x, y, z) in xy – plane yz – plane, and xz plane is (x, y, –z), (–x, y, z), (x,–y, z) respectively.
- Coordinates of a point P are the perpendicular distances of P from three coordinate planes YZ, ZX and XY respectively.

##### Important Extra Questions with Answer

- Find the image of (–5, 4, –3) in xz plane. [Answer: (-5, -4, -3)]
- Name the octant in which (–5, 4, –3) lies. [Answer: OX’YZ’]
- Let A, B, C be the feet of perpendiculars from point P on the xy, yz and xz planes respectively. Find the coordinates of A, B, C where the point P is (4, –3, –5). [Answer: (4, –3, 0), (0, –3, –5), (4, 0, –5)]
- What is the perpendicular distance of the point P(6, 7, 8) from xy plane. [Answer: 8]
- If the distance between the points (a, 2, 1) and (1, –1, 1) is 5, then find the value (s) of a. [Answer: 5, -3]
- What are the coordinates of the vertices of a cube whose edge is 2 unit, one of whose vertices coincides with the origin and the three edges passing through the origin? Coincides with the positive direction of the axes through the origin? [Answer: (2, 0, 0), (2, 2, 0), (0, 2, 0), (0, 2, 2), (0, 0, 2), (2, 0, 2), (0, 0, 0), (2, 2, 2)]
- If a parallelepiped is formed by planes drawn through the point (5, 8, 10) & (3, 6, 8) parallel to the coordinates planes, then find the length of the diagonal of the parallelepiped. [Answer: 2√3]
- Find the length of the longest piece of a string that can be stretched straight in a rectangular room whose dimensions are 13, 10 and 8 unit. [Answer: √333]
- Find the distance of point P(3, –2,1) from z–axis. [Answer: √13]
- Write coordinates of foot of perpendicular from (3, 7, 9) on x axis y-axis, z-axis. [Answer: (3, 0, 0)]