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RS Aggarwal Class 11 Chapter 26 Solutions (Three Dimensional Geometry)

RS Aggarwal Class 11 Solution for Chapter 26 is a perfect guide for you to learn the basic concepts of Three Dimensional Geometry. Chapter 26 is a very important Chapter for Class 11 as it makes up the base for CBSE Class 12. This Chapter is a little difficult but RS Aggarwal Class 11 Maths Solutions make the Chapter easy for students and hence clear their concepts related to the Chapter.

The Chapter consists of 3 exercises with 18 questions in it. Each topic along with the exercise questions contains several solved examples which you can practise so as to clear the concept and master the topic. The Solutions are designed in a systematic step by step so as to make it easy.

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Important Points of Chapter 26 – Three Dimensional Geometry

  • A coordinate system which specifies each point uniquely in a plane by a pair of numerical coordinates is known as Cartesian Plane
  • A pair of numbers that define its exact location on a 2-D plane is known as the coordinates of a point 
  • A number on the x-axis is known as the x-coordinate
  • A number on the y-axis is known as the y-coordinate
  • The pair which contains the coordinates of a point in the coordinate system is known as the ordered pair
  • The x-coordinate is always first, followed by the y-coordinate
  • A 1-dimensional coordinate system is known as a number line
  • The coordinates are always written as an ordered pair 
  • The 3 planes determined by the pair of axes are known as the coordinate planes
  • The 8 parts formed when the 3 coordinate planes divide are known as Octants
  • Any 3 numbers proportional to the direction cosines are known as the direction ratios of that line

Topics Covered Under Chapter 26 Three Dimensional Geometry

The following different topics are covered under this Chapter:

  • Coordinate Axes
  • Coordinate Planes
  • Coordinate of point in space
  • Planes
  • Octants 
  • Cartesian plane
  • Ordered pair
  • Points in 3D
  • One-Dimensional coordinate system
  • Two-Dimensional coordinate systems
  • Distance between 2 points
  • Section formula
  • Coordinates of a triangle
  • Distance formula
  • Distance formula between 2 points

Some Important Methods and Formulas

  1. Coordinates of any point on
  • x-axis is of the form (x, 0, 0)
  • Y-axis is of the form (0, y, 0)
  • Z-axis is of the form (0, 0, z)
  • XY-plane are of the form (x, y, 0)
  • YZ-plane is of the form (0, y, z)
  • ZX-plane are of the form (x, 0, z)
  1. Distance Formula
  • The distance between 2 points P(X1,Y1,Z1) and Q(X2,Y2,Z2) is given by PQ = (X2-X1)² + (Y2-Y1)² + (Z2-Z1)²
  • The distance of point P(x, y, z)  from the origin O(0,0,0) is given by OP = x² + y² + z²

Exercise Wise Discussion of RS Aggarwal Class 11 Chapter 26 Three Dimensional Geometry

Exercise 26A

This exercise 26A has 4 questions in which you have to:

  • Find x and y coordinates when a point is given
  • Find the plane from the given points
  • Find the octant of the given point

Exercise 26B

This exercise 26B has 8 questions in which you have to:

  • Find the distance between the given points
  • Show the given points as the vertices of different types of triangles
  • Show the given points as the vertices of closed figures like square, parallelogram, rhombus and rectangle

Exercise 26C

This exercise 26C has 6 questions in which you have to:

  • Find the coordinates of points which divides the given points in the given ratio
  • Find the coordinates of the point of trisection of a line where coordinates of the line segment are given.
  • Find the ratio in which given points divides the line
  • Find the ratio in which line segment is divided by the plane
  • Find the coordinates of the points of division

Benefits of RS Aggarwal Class 11 Chapter 26

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