A tow rope pulls a barge with the force F = 2 i - 3 j + 6 k kilonewtons…

A vector $x\hat i + y\hat j + z\hat k$ has magnitude $\sqrt{x^2 + y^2 + z^2}$ and unit vector $\hat a = \dfrac{\vec a}{\lvert\vec a\rvert}$. Its direction cosines are $l = \dfrac{x}{\lvert\vec a\rvert}$, $m = \dfrac{y}{\lvert\vec a\rvert}$, $n = \dfrac{z}{\lvert\vec a\rvert}$, and $l^2 + m^2 + n^2 = 1$.