JEE Main 2024 (Online) 6th April Morning ShiftQuestion 1
Let $P$ be the point $(10,-2,-1)$ and $Q$ be the foot of the perpendicular drawn from the point $R(1,7,6)$ on the line passing through the points $(2,-5,11)$ and $(-6,7,-5)$. Then the length of the line segment $PQ$ is equal to $\_\_\_\_\_\_$ .
3D Geometry
Answer$13$
Solution
Line: $(2,-5,11)+t(2,-3,4)$. $\vec{AR}=(-1,12,-5)$, dot $=-58$, $t=-2$, so $Q=(-2,1,3)$. $PQ=\sqrt{144+9+16}=13$.