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7. The points $A(−1,1,1),B(2,0,3)$, and $C(3,3,−4)$ are vertices of a triangle. a. Show that this triangle is a right triangle. b. Calculate the area of triangle $ABC$. c. Calculate the perimeter of triangle $ABC$. d. Calculate the coordinates of the fourth vertex $D$ that completes the rectangle of which $A,B$, and $C$ are the other three vertices.

Solution:

Given vertices of a triangle are

Lengths of sides

(a).

Thus

Given vertices form a right-angled triangle

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