Chapter 12: Vectors and the Geometry of Space - Section 12.2 - Vectors - Exercises 12.2 - Page 705: 33

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

Formula to calculate the unit vector $\hat{\textbf{u}}$ is: $\hat{\textbf{u}}=\dfrac{u}{|u|}$ Given: $u=12i +0j-5k$; $|u|=\sqrt{(12)^2+(0)^2+(-5)^2}=\sqrt{144+25}=\sqrt {169}=13$ Thus, $\hat{\textbf{u}}=\dfrac{12i +0j-5k}{13}=(\dfrac{12}{13}i +0j -\dfrac{5}{13}k)$ and, $7\hat{\text{u}}=\dfrac{7}{13}(12i-5k)$