How do you find the unit vector having the same direction as vector u = i - 6 j + 5 k?

Jul 1, 2016

Thus $\text{ } \hat{u} = \frac{1}{\sqrt{61}} i - \frac{6}{\sqrt{61}} j + \frac{5}{\sqrt{61}} k$

Or if you prefer

$\text{ } \hat{u} = \frac{\sqrt{61}}{61} i - \frac{6 \sqrt{61}}{61} j + \frac{5 \sqrt{61}}{61} k$

Explanation:

Given that $\vec{u} = i - 6 j + 5 k$

Then $| | u | | = \sqrt{{1}^{2} + {\left(- 6\right)}^{2} + {5}^{2}} \text{ "=" } \sqrt{61}$

Not that 61 is a prime number

Thus $\text{ } \hat{u} = \frac{1}{\sqrt{61}} i - \frac{6}{\sqrt{61}} j + \frac{5}{\sqrt{61}} k$

Or if you prefer

$\text{ } \hat{u} = \frac{\sqrt{61}}{61} i - \frac{6 \sqrt{61}}{61} j + \frac{5 \sqrt{61}}{61} k$