Question

The name of the figure formed by the points $(-2,4,1),(-1,5,5),(2,2,5)$ and $(1,1,1)$ is a

• A. rectangle
• B. rhombus
• C. square
• D. parallelogram

Answer 1

Answer: (C)

square

Given Points : $A(-2,4,1),B(-1,5,5),C(2,2,5),D(1,1,1)$
Dot product of direction ratios of diagonals $AC$ and $BD:$ $(4,-2,4).(2,-4,-4)=0$
Figure is either square or rhombus.
Dot product of direction ratios of $AB$ and $BC:$$(1,1,4).(3,-3,0)=0$
Figure is square.