Minimum distance between a line and an ellipsoid

Given the ellipsoid

$\dfrac{x^2}{5^2} + \dfrac{y^2}{7^2} + \dfrac{z^2}{10^2} = 1$

and a spatial line whose parametric equation is given by $\mathbf{p}(t) = \mathbf{p}_0 + t \mathbf{d}$ , where $\mathbf{p}_0 = (5, 7, 10)$ , $\mathbf{d} = (1, -1, 1)$ , and $t \in \mathbb{R}$ is an arbitrary parameter, we want to find the minimum distance $d^*$ , between a point $P =(x_1, y_1, z_1 )$ on the line and a point $Q = (x_2, y_2, z_2 )$ on the ellipsoid. If the minimum occurs with $P^* = ({x_1}^*,{y_1}^*,{z_1}^*)$ , and $Q^* = ( {x_2}^*,{y_2}^*,{z_2}^*)$ , then report the value of $\lfloor 100({x_1}^*+{y_1}^*+{z_1}^* + {x_2}^*+{y_2}^*+{z_2}^* + d^* ) \rfloor$ , where $\lfloor \cdot \rfloor$ is the floor function, for example, $\lfloor 7.6 \rfloor = 7$ .