Login/Sign Up
Home » Prove that the triangle formed by joining the three points whose coordinates are (1, 2, 3), (2, 3, 1) and (3, 1, 2) is an equilateral triangle.
Prove that the triangle formed by joining the three points whose coordinates are (1, 2, 3), (2, 3, 1) and (3, 1, 2) is an equilateral triangle.
CBSE | Class 11 | Exercise 28.2 | Introduction to Three Dimensional Coordinate Geometry | Maths | RD Sharma
Prove that the triangle formed by joining the three points whose coordinates are (1, 2, 3), (2, 3, 1) and (3, 1, 2) is an equilateral triangle.

Given:

The points

    \[\left( 1,\text{ }2,\text{ }3 \right),\text{ }\left( 2,\text{ }3,\text{ }1 \right)\text{ }and\text{ }\left( 3,\text{ }1,\text{ }2 \right)\]

An equilateral triangle is a triangle whose all sides are equal.

So let us prove

    \[AB\text{ }=\text{ }BC\text{ }=\text{ }AC\]

By using the formula,

The distance between any two points

    \[\left( a,\text{ }b,\text{ }c \right)\text{ }and\text{ }\left( m,\text{ }n,\text{ }o \right)\]

is given by,

RD Sharma Solutions for Class 11 Maths Chapter 28 – image 26

RD Sharma Solutions for Class 11 Maths Chapter 28 – image 27

It is clear that,

    \[AB\text{ }=\text{ }BC\text{ }=\text{ }AC\]

    \[\Delta \text{ }ABC\]

is a equilateral triangle

Hence Proved.

i

More Material