Mathematics

Problem

Consider the points

P(1,1,1)

Q(1,-1,-1)

and

R(-1,1,-1)

\mathbb R^{3}

. a. (i) Compute the lengths

PQ,QR

and

RP

. b. (ii) Hence decide the type of triangle formed by

P,Q

and

R

(equilateral, isosceles or scalene). c. (iii) Determine the exact perimeter of

\triangle PQR