Question 1067844
{{{A(1,2,3)}}}
{{{B(-1,-2,-1)}}}
{{{C(2,3,2)}}}
{{{D(4,7,6)}}}
The vector from {{{B}}} to {{{A}}} is
{{{(matrix(1,5,1," ",2," ",3))-(matrix(1,5,-1," ",-2," ",-1))=(matrix(1,5,1-(-1)," ",2-(-2)," ",3-(-1)))=(matrix(1,5,2," ",4," ",4))}}} .
The vector from {{{C}}} to {{{D}}} is the same:
{{{(matrix(1,5,4," ",7," ",6))-(matrix(1,5,2," ",3," ",2))=(matrix(1,5,4-2," ",7-3," ",6-2))=(matrix(1,5,2," ",4," ",4))}}} ,
So AB and DC area parallel,
going in the same direction,
and with the same length,
That makes ABCD a parallelogram.
To be a rectangle the diagonals AC and BD should have the same length.
However, their length squared are different:
{{{AC^2=(2-1)^2+(3-2)^2+(2-3)^2=1^2+1^2+(-1)^2=1+1+1=3}}} and
{{{BC^2=(4-(-1))^2+(7-(-2))^2+(6-(-1))^2=5^2+9^2+7^2<>1}}}