Chapter 11 - Section 11.2 - Vectors - Exercises - Page 609: 33

$\dfrac{7}{13}(12i-5k)$

Here, $u=12i +0j-5k$ and $|u|=\sqrt{(12)^2+(0)^2+(-5)^2}=\sqrt {1}=\sqrt {169}=13$ The unit vector $\hat{\textbf{u}}$ can be calculated as: $\hat{\textbf{u}}=\dfrac{u}{|u|}$ Now, $\hat{\textbf{u}}=\dfrac{12i +0j-5k}{13}=(\dfrac{12}{13}i +0j -\dfrac{5}{13}k)$ Thus, $7\hat{\textbf{u}}=\dfrac{7}{13}(12i-5k)$