$\vec{N} \bullet (\vec{v} - \vec{v}_0) = 0 \ \vec{N} \bullet (\vec{C} + t \cdot \vec{d} - \vec{v}_0) = 0 \ \vec{N} \bullet (\vec{C} - \vec{v}_0) + t \cdot \vec{N} \bullet \vec{d} = 0 \ t \cdot \vec{N} \bullet \vec{d} = - \vec{N} \bullet (\vec{C} - \vec{v}_0) \ t = - \frac{\vec{N} \bullet (\vec{C} - \vec{v}_0)}{\vec{N} \bullet \vec{d}} \$