Question

Show that the points (1, 2, 3); (2, 3, 1) and (3, 1, 2) form an equilateral triangle ​

Answer 1

Answer:

ABC is an equilateral triangle

Step-by-step explanation:

Let the points be A : (1,2,3) , B : (2,3,1) & C : (3,1,2)

Therefore , let the equilateral triangle be ABC

Distance = √ (X2 - X1)^2 + (Y2 - Y1)^2 + (Z2 -Z1)^2

AB = √ ( 2 - 1 )^2 + ( 3 - 2 )^2 + ( 1 - 3 )^2

= √ 1 + 1 + 4

= √ 6

Therefore , AB = √ 6

BC = √ ( 3 - 2 )^2 + ( 1 - 3 )^2 + ( 2 - 1 )^2

= √ 1 + 4 +1

= √ 6

Therefore , BC = √ 6

AC = √ ( 3 - 1 )^2 + ( 1 - 2 )^2 + ( 2 - 3 )^2

= √ 4 + 1 + 1

= √ 6

Therefore , AC = √ 6

Hence , AB = BC = AC = √6

Since , three sides are equal , triangle ABC is an equilateral triangle.

Hence prooved.