Answer
We can calculate the length of the sides of triangle using the distance formula
P(3,-2,-3) Q(7,0,1) R(1,2,1)
now calculate the distance between lines |PQ|,|PR|,|QR|
Work Step by Step
|PR|= $\sqrt ((1- 3)^2+(2+2)^2+ (1+3)^2)$
|PR|= $\sqrt (16+16+4)$
|PR|=$ \sqrt 36$
|PR|=6
|PQ|= $\sqrt ((7- 3)^2+(0+2)^2+ (1+3)^2)$
|PQ|= $\sqrt (16+16+4)$
|PQ|=$ \sqrt 36$
|PQ|=6
|QR|= $\sqrt ((1- 7)^2+(2-0)^2+ (1-1)^2)$
|QR|= $\sqrt (36+4-0)$
|QR|=$ \sqrt 46$
|QR|=2$\sqrt 10$
sides are |PQ|=|PR|=6 |QR|=2$\sqrt 10$
Since two sides are similar triangle PQR is an isosceles triangle
