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
- 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.
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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