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

Question

If $P(0,7,10), Q(-1,6,6)$ and $R(-4,9,6)$ are three points in the space, then $P Q R$ is, right angled isosceles triangle, equilateral triangle, isosceles but not right angled triangle, scalene triangle

MARKS App · Accepted Answer

Given points $P(0,7,10), Q(-1,6,6)$ and $R(-4,9,6)$ $\begin{aligned} & \therefore P Q=\sqrt{1+1+16}=\sqrt{18}=3 \sqrt{2} \ & Q R=\sqrt{9+9+0}=\sqrt{18}=3 \sqrt{2} \ & \text { and } P R=\sqrt{16+4+16}=\sqrt{36}=6 \ & \because P Q^2+Q R^2=18+18=36=P R^2 \text { and } P Q=Q R \end{aligned}$ $\therefore P Q R$ is a right angled isosceles triangle. Hence, option (1) is correct.

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