If P(0, 7, 10),Q(-1, 6, 6),and R(-4, 9, 6) ar | vedclass

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(A) Given points are $P(0, 7, 10)$,$Q(-1, 6, 6)$,and $R(-4, 9, 6)$.Using the distance formula $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}$:$PQ

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right-angled isosceles triangle

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(A) Given points are $P(0, 7, 10)$,$Q(-1, 6, 6)$,and $R(-4, 9, 6)$.Using the distance formula $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}$:$PQ = \sqrt{(-1-0)^2 + (6-7)^2 + (6-10)^2} = \sqrt{1 + 1 + 16} = \sqrt{18} = 3\sqrt{2}$.$QR = \sqrt{(-4 - (-1))^2 + (9-6)^2 + (6-6)^2} = \sqrt{(-3)^2 + 3^2 + 0^2} = \sqrt{9 + 9 + 0} = \sqrt{18} = 3\sqrt{2}$.$PR = \sqrt{(-4-0)^2 + (9-7)^2 + (6-10)^2} = \sqrt{(-4)^2 + 2^2 + (-4)^2} = \sqrt{16 + 4 + 16} = \sqrt{36} = 6$.Since $PQ = QR = 3\sqrt{2}$,the triangle is isosceles.Also,$PQ^2 + QR^2 = 18 + 18 = 36 = PR^2$. By the converse of the Pythagorean theorem,$	riangle PQR$ is a right-angled triangle.Therefore,$	riangle PQR$ is a right-angled isosceles triangle.

If $P(0, 7, 10)$,$Q(-1, 6, 6)$,and $R(-4, 9, 6)$ are three points in space,then $\triangle PQR$ is:

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