Two supports in a stadium roof lie along the lines (x + 2)/2 = (y - 3)/3 = (z - 4)/6 and x/3 = (y…

Step 1. The cross product. $\vec{b}_1 \times \vec{b}_2 = (3 \times 2 - 6 \times (-6),\ 6 \times 3 - 2 \times 2,\ 2 \times (-6) - 3 \times 3) = (42, 14, -21)$. Its length is $\sqrt{1764 + 196 + 441} = 49$.

Step 2. The triple product. $(2, 1, -7) \cdot (42, 14, -21) = 84 + 14 + 147 = 245$.

Step 3. The distance. $d = \dfrac{245}{49} = 5$ metres.

Step 4. The bar. The direction cosines are $\dfrac{42}{49}$, $\dfrac{14}{49}$ and $\dfrac{-21}{49}$, which are $\dfrac{6}{7}$, $\dfrac{2}{7}$ and $-\dfrac{3}{7}$. So $l = \dfrac{6}{7} \approx 0.857$.