The points A(-1, 2, 3),B(2, -3, 1),and C(3, 1 | vedclass

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(D) To determine the nature of the triangle formed by points $A(-1, 2, 3)$,$B(2, -3, 1)$,and $C(3, 1, -2)$,we calculate the lengths of the sides using

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form a scalene triangle

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(D) To determine the nature of the triangle formed by points $A(-1, 2, 3)$,$B(2, -3, 1)$,and $C(3, 1, -2)$,we calculate the lengths of the sides using the distance formula $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}$.$1$. Length of $AB$:$AB = \sqrt{(2 - (-1))^2 + (-3 - 2)^2 + (1 - 3)^2} = \sqrt{3^2 + (-5)^2 + (-2)^2} = \sqrt{9 + 25 + 4} = \sqrt{38}$.$2$. Length of $BC$:$BC = \sqrt{(3 - 2)^2 + (1 - (-3))^2 + (-2 - 1)^2} = \sqrt{1^2 + 4^2 + (-3)^2} = \sqrt{1 + 16 + 9} = \sqrt{26}$.$3$. Length of $AC$:$AC = \sqrt{(3 - (-1))^2 + (1 - 2)^2 + (-2 - 3)^2} = \sqrt{4^2 + (-1)^2 + (-5)^2} = \sqrt{16 + 1 + 25} = \sqrt{42}$.Since all sides $AB = \sqrt{38}$,$BC = \sqrt{26}$,and $AC = \sqrt{42}$ are unequal,the triangle is a scalene triangle.

The points $A(-1, 2, 3)$,$B(2, -3, 1)$,and $C(3, 1, -2)$:

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