# How do you find a unit vector in the direction of 3i+4j-k?

Sep 18, 2016

$\frac{3 i + 4 j - k}{\sqrt{26}}$

#### Explanation:

We have: $3 i + 4 j - k$

Let $u = 3 i + 4 j - k$.

Unit vectors are of the form $\hat{u} = \frac{u}{\left\mid u \right\mid}$:

$\implies \hat{u} = \frac{3 i + 4 j - k}{\left\mid 3 i + 4 j - k \right\mid}$

$\implies \hat{u} = \frac{3 i + 4 j - k}{\sqrt{{3}^{2} + {4}^{2} + {\left(- 1\right)}^{2}}}$

$\implies \hat{u} = \frac{3 i + 4 j - k}{\sqrt{9 + 16 + 1}}$

$\implies \hat{u} = \frac{3 i + 4 j - k}{\sqrt{26}}$