The points A(5, - 1, 1) B(7, - 4,7),C(1, - 6, 10) and D(1 - 3,4) are vertices of a

Given that, A(5, - 1, 1) B(7, - 4,7),C(1, - 6, 10) and D(1 - 3,4)now,AB=(7−5)2+(−4+1)2+(7−1)2=4+9+36=7BC=(1−7)2+(−6+4)2+(10−7)2=36+4+9=7CD=(−1−1)2+(−3+6)2+(4−10)2=4+9+36=7DA=(5+1)2+(−1+3)2+(1−4)2=36+4+9=7∴ AB=BC=CD=DA=7,Also, AC=(1−5)2+(−6+1)2+(10−1)2=16+25+81=122BD=(−1−7)2+(−4+3)2+(7−4)2=64+1+9=74Diagonal AC≠BDHence, ABCD is not a square, so it is a rhombus.