Introduction to 3-D Geometry ISC Class-11 Maths ML Aggarwal Solutions

Introduction to 3-D Geometry ISC Class-11 Maths ML Aggarwal Solutions Chapter-2. Step by step Solutions of ML Aggarwal ISC Class-11 Mathematics with Exe-2.1, Exe-2.2, Exe-2.3, and Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-11 Mathematics.

Introduction to 3-D Geometry ISC Class-11 Maths ML Aggarwal Solutions

Introduction to 3-D Geometry ISC Class-11 Maths ML Aggarwal Solutions Chapter-2

Board   ISC
Class  11
Subject Mathematics
Chapter- Introduction to 3-D Geometry
Session  2024-25
Topics  Solutions of ML Aggarwal

Introduction to 3-D Geometry

Coordinate Axes:  In three dimensions, the coordinate axes of a rectangular cartesian coordinate system are three mutually perpendicular lines. These axes are called the X, Y and Z axes.

Coordinate Planes:  The three planes determined by the pair of axes are the coordinate planes. These planes are called XY, YZ and ZX plane and they divide the space into eight regions known as octants.

Coordinates of a Point in Space :

The coordinates of a point in the space are the perpendicular distances from P on three mutually perpendicular coordinate planes YZ, ZX, and XY respectively. The coordinates of a point P are written in the form of triplet like (x, y, z).
The 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)

Note :-

  1. Points are defined as the triples of real numbers arranged in an order such as P1 = (x1, y1, z1) and P2 = (x2, y2, z2)
  2. A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
  3. The coordinates of a point are a pair of numbers that define its exact location on a two-

dimensional plane A number on the x-axis called an x-coordinate, and a number on the y-axis called a y-coordinate.

An ordered pair contains the coordinates of one point in the coordinate system.

The order in which you write x- and y-coordinates in an ordered pair is very important.

The x-coordinate always comes first, followed by the y-coordinate There is also a three coordinate called Z coordinate

Formula for Distance Between Two Points

  • Distance between two points is given by formula = √[(x2 – x1)2 + (y2 – y1)2 ]
  • Distance between three two points = [(x2 – x1)2 + (y2 – y1)2 + (z2 – z1)2]

Section Formula

  • Coordinates of point P(x, y) that divides the line segment joining the points A(x1, y1) and B(x2, y2) internally in the ratio m1: m2 are m1x2 + m2x1/m1+ m2 and m1x2 + m2x1/m1+ m2
  • The mid-point of the line segment joining the points A(x1, y1) and B(x2, y2) can be found by [(x1 + x2/2) , (y1+ y2)/2].

Centroid of the Triangle

The centroid of the triangle with vertices A(x1, y1, z1), B(x2, y2, z2) and C(x3, y3, z3) = . ((x1+x2+x3)/3, (y1+y2+y3)/3, (z1+z2+z3)/3

 


Exe-2.1

Introduction to 3-D Geometry ISC Class-11 Maths ML Aggarwal Solutions Chapter-2


Exe-2.2

Introduction to 3-D Geometry ISC Class-11 Maths Solutions Chapter-2


Exe-2.3

Chapter-2 Introduction to 3-D Geometry Class-11 Maths


Chapter Test

 Introduction to 3-D Geometry Class-11 Maths

-: End of Chapter-2 Introduction to 3-D Geometry Class-11 Maths  :-

Return to :- ML Aggrawal ISC Class-11 Vol-2 Maths Solutions

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