A pipeline runs in the direction b = i + 2 j + 2 k…

Step 1. The dot product. $\vec a\cdot\vec b = 4 - 6 + 10 = 8$, and $\lvert\vec b\rvert = \sqrt{1 + 4 + 4} = 3$.

Step 2. The projection. The scalar projection is $\dfrac{8}{3} \approx 2.67$ kilonewtons.

Step 3. The part across. $\lvert\vec a\rvert^2 = 16 + 9 + 25 = 50$. So $\lvert\vec a_{\perp}\rvert^2 = 50 - \dfrac{64}{9} = \dfrac{386}{9}$, and $\lvert\vec a_{\perp}\rvert = \dfrac{\sqrt{386}}{3} \approx 6.55$ kilonewtons.