A(1,2,-1), B(2,5,-2) and C(4,4,-3) are three vertices of a rectangle. What is the area of the rectangle?

Explanation

The length of AB = \sqrt{(2-1)^2 + (5-2)^2 + (-2+1)^2} = \sqrt{1 + 9 + 1} = \sqrt{11}. The length of BC = \sqrt{(4-2)^2 + (4-5)^2 + (-3+2)^2} = \sqrt{4 + 1 + 1} = \sqrt{6}. The area of the rectangle is AB \times BC = \sqrt{11} \times \sqrt{6} = \sqrt{66} square units.

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