Vertices of the quadrangle are A(−3,5,6),B(1,−5,7),C(8,−3,−1) and D(4,7,−2)
Let's find out length of the sides of the quadrangle
To find AB,BC,CD and AD
AB=√(1+3)2+(−5−5)2+(7−6)2=√16+100+1=√117
BC=√(8−1)2+(−3+5)2+(−1−7)2=√49+4+64=√117CD=√(4−8)2+(7+3)2+(−2+1)2=√16+100+1=√117
AD=√(−3−4)2+(5−7)2+(6+2)2=√49+4+64=√117
Length of all sides are equal
Also, find the length of diagonals
AC=√(8+3)2+(−3−5)2+(−1−6)2=√121+64+49=√234
BD=√(4−1)2+(7+5)2+(−2−7)2=√9+144+81=√234
Thus, the lengths of diagonals are equal
Hence, the quadrangle formed by A,B,C and D is a square.