Distance AB:
A= (5, 4, −1), B= (3, 6, −1)
AB = \(\sqrt {{{(3 - 5)}^2} + {{\left( {6 - 4} \right)}^2} + {{\left( { - 1 + 1} \right)}^2}} \)
=\(\sqrt {4 + 4 + 0} \)
= \(\sqrt 8 \) units
Distance BC:
B= (3, 6, −1) ,C=(3, 4, 1)
BC =\(\sqrt {{{(3 - 3)}^2} + {{\left( {4 - 6} \right)}^2} + {{\left( { 1 + 1} \right)}^2}} \)
= \(\sqrt {0 + 4 + 4} \)
= \(\sqrt 8 \) units
Distance AC:
A= (5, 4, −1) ,C=(3, 4, 1)
AC = \(\sqrt {{{(3 - 5)}^2} + {{\left( {4 - 4} \right)}^2} + {{\left( { 1 + 1} \right)}^2}} \)
=\(\sqrt {4 + 0 + 4} \)
= \(\sqrt 8 \) units
Here the sides of triangle ABC are equal in length.
Therefore, the given triangle is an equilateral triangle.