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Find a vector in the direction of vector  \(2\hat i-3\hat j+6\hat k\)  which has magnitude 21 units.

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Given that  \(\vec a=2\hat i-3\hat j+6\hat k\)

The unit vector of any vector  \(\vec a=a_1\hat i+a_2\hat j+a_3\hat k\) can be written as

Let the required vector be  \(\vec d\).

Any vector ( \(\vec p\)) with magnitude m and unit vector  \(\hat a\)  can be written as  \(\vec p=m\times\hat a.\)

Since the magnitude of \(\vec d\)is 21 and it's unit vector is  \(\hat a,\)  we get

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