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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.

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