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.

Asked by Sakshi | 1 year ago |  45

1 Answer

Solution :-

Given:

The points (1, 2, 3), (2, 3, 1) and (3, 1, 2)

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

So let us prove AB = BC = AC

By using the formula,

The distance between any two points (a, b, c) and (m, n, o) is given by,

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

\( \sqrt{6}\)

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

It is clear that,

AB = BC = AC

Δ ABC is a equilateral triangle

Hence Proved.

Answered by Aaryan | 1 year ago

Related Questions

A(1, 2, 3), B(0, 4, 1), C(-1, -1, -3) are the vertices of a triangle ABC. Find the point in which the bisector of the angle ∠BAC meets BC.

Class 11 Maths Introduction to Three Dimensional Geometry View Answer

The mid-points of the sides of a triangle ABC are given by (-2, 3, 5), (4, -1, 7) and (6, 5, 3). Find the coordinates of A, B and C.

Class 11 Maths Introduction to Three Dimensional Geometry View Answer

Find the ratio in which the line segment joining the points (2, -1, 3) and (-1, 2, 1) is divided by the plane x + y + z = 5.

Class 11 Maths Introduction to Three Dimensional Geometry View Answer