Let $l$ be the line passing through two distinct points $\mathrm { A } , \mathrm { B }$ on plane $\alpha$, and let H be the foot of the perpendicular from point P (not on plane $\alpha$) to plane $\alpha$. When $\overline { \mathrm { AB } } = \overline { \mathrm { PA } } = \overline { \mathrm { PB } } = 6 , \overline { \mathrm { PH } } = 4$, what is the distance between point H and line $l$? [3 points] (1) $\sqrt { 11 }$ (2) $2 \sqrt { 3 }$ (3) $\sqrt { 13 }$ (4) $\sqrt { 14 }$ (5) $\sqrt { 15 }$
Let $l$ be the line passing through two distinct points $\mathrm { A } , \mathrm { B }$ on plane $\alpha$, and let H be the foot of the perpendicular from point P (not on plane $\alpha$) to plane $\alpha$. When $\overline { \mathrm { AB } } = \overline { \mathrm { PA } } = \overline { \mathrm { PB } } = 6 , \overline { \mathrm { PH } } = 4$, what is the distance between point H and line $l$? [3 points]\\
(1) $\sqrt { 11 }$\\
(2) $2 \sqrt { 3 }$\\
(3) $\sqrt { 13 }$\\
(4) $\sqrt { 14 }$\\
(5) $\sqrt { 15 }$