## NCERT Solutions for Class 11 Maths Three Dimensional Geometry

**NCERT Solutions for Class 11 Maths** : Takshila Learning offers **Class 11 Maths** **NCERT solutions**. NCERT Solutions are an important part of learning for those who want to score well in their Class 11th^{ }Maths exam. The series of chapters includes solutions to all questions and helps students to prepare well and score good marks. Register with Takshila Learning and get easy access to **CBSE Class 11 Online classes **with NCERT solutions for all the chapters in a chapter wise manner.In the following article, we are going to discuss “Three-diamensional geometry” from *Class 11th Maths*.

**Three dimensional geometry Coordinate axes and coordinate planes:**

Let X′OX, Y′OY, Z′OZ be three mutually perpendicular lines that pass through a point O(origin) such that X′OX and Y′OY lie in the plane of the paper and line Z′OZ is perpendicular to the plane of the paper.

- In three dimensions, the coordinate axes of a rectangular Cartesian coordinate

system are three mutually perpendicular lines. The axes are called the x, y

and z-axes.

- The three axes taken together in pairs determine three coordinate planes iexy, yz and zx-planes.

- The three coordinate planes divide the space into eight parts known as
**octants**and named as XOYZ, X′OYZ, X′OY′Z, XOY′Z, XOYZ′, X′OYZ′, X′OY′Z′ and XOY′Z′. and denoted by I, II, III, …, VIII respectively.

- The coordinates of an arbitrary point P in three-dimensional geometry is written

in the form of triplet ie (x, y, z). Here x, y,and z are the distances from the

yz**, **zx and xyplanes. If there is a point on x axis then its coordinates are (x,0,0)

**Sign of coordinates of a point:** The sign of the coordinates of a point depends upon the octant in which it lies.

Octants→ Coordinates ↓ | I XOYZ | II X′OYZ | III X′OY′Z | IV XOY′Z | V XOYZ′ | VI X′OYZ′ | VII X′OY′Z′ | VIII XOY′Z′ |

x | + | - | - | + | + | - | - | + |

y | + | + | - | - | + | + | - | - |

z | + | + | + | + | - | - | - | - |

*For practice sets of Three-dimensional geometry& more, click on ***NCERT Maths Class 11.**

**Question:** What are the coordinates of a point lying in YZ plane?

**Solution:** Since the point is in YZ plane so its x coordinate is ‘0’.So the coordinate is of the form (0,y,z).

**Question: **Name the octants in which the following points lie:

(3,5,6) , (-5,-9,7) , (-3,5,8) , (-6,-8,-2)

**Solution: **Using thetable we have

(3,5,6) → I (-5,-9,7) → III

(-3,5,8)→ II (-6,-8,-2)→ VII

**Question:** What is the locus of a point for which x= 0, y= 0?

**Solution: **The locus is z axis since on z axis x and y coordinates are zero.

** **

**Question: **What does x = 0 and x = a represent?

**Solution: **x = 0 represents yz plane and x = a represents a plane parallel to yz plane at a distance of ‘a’ from origin.

**Question: **The intersection of two planes xy-plane and xzplaneis?

**Solution: **xy-plane and xzplane intersects at x axis.

**Question: **Let A, B, C be the feet of the perpendiculars drawn from a point P (3, 7, 5)

on the *x*, *y *and *z*-axes respectively. Find the coordinates of A, B, and C.

**Solution: **Since A is the foot of perpendicular from P on the *x*-axis, its *y *and *z *coordinates

are zero. The coordinates of A are (3, 0, 0). Similarly, the coordinates of B and

C are (0, 7, 0) and (0, 0, 5), respectively.

**Question: **Let A be the foot of the perpendicular drawn from a point (1,2,3) on xyplane. What are the coordinates of A?

**Solution: ** SinceA is the foot of the perpendicular of the point on xy plane so its z coordinate is zero. the coordinates of A are (1,2,0).

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