# Find the unit vector in the direction of vector $\rm \vec{a}= 3\hat i -4\hat j+12\hat k$

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Find the unit vector in the direction of vector $\rm \vec{a}= 3\hat i -4\hat j+12\hat k$
1. $\rm \frac{3}{13} \hat i + \frac{4}{13} \hat j + \frac{12}{13} \hat k$
2. $\frac{1}{9} \hat i - \frac{4}{9} \hat j + \frac{8}{9} \hat k$
3. $\rm \frac{3}{13} \hat i - \frac{4}{13} \hat j + \frac{12}{13} \hat k$
4. $\rm \frac{3}{13} \hat i + \frac{4}{13} \hat j - \frac{12}{13} \hat k$

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Correct Answer - Option 3 : $\rm \frac{3}{13} \hat i - \frac{4}{13} \hat j + \frac{12}{13} \hat k$

Concept:

The unit vector in the direction of vector $\rm \vec{z}$ is given by $\hat z = \rm \frac{\vec{z}}{|z|}$.

Calculation:

Given: $\rm \vec{a}= 3\hat i -4\hat j+12\hat k$

As we know that unit vector in the direction of vector $\rm \vec{a}$ is given by $\hat a = \rm \frac{\vec{a}}{|a|}$.

⇒ $\rm \vec{a} = \rm \frac{3\hat i-4\hat j+12\hat k}{\sqrt{3^2+4^2+12^2}}$

⇒ $\rm \vec{a} = \frac{3}{13} \hat i - \frac{4}{13} \hat j + \frac{12}{13} \hat k$

Hence, option 3 is correct.