# Chapter 9 - Polar Coordinates; Vectors - 9.6 Vectors in Space - 9.6 Assess Your Understanding - Page 625: 47

$\frac{3}{7}i-\frac{6}{7}j-\frac{2}{7}k.$

#### Work Step by Step

If $v=ai+bj+ck$ and $||v||=\sqrt{a^2+b^2+c^2}$, then the unit vector $u$ in the same direction as $v$ is $u=\frac{v}{||v||}$. The magnitude of $v$ is $||v||=\sqrt{3^2+(-6)^2+(-2)^2}\\||v||=\sqrt{9+36+4}\\||v||=\sqrt{49}=7.$ Thus the unit vector is: $u=\frac{3i-6j-2k}{7}\\u=\frac{3}{7}i-\frac{6}{7}j-\frac{2}{7}k.$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.