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If  \(\vec a=\hat i+2\hat j-3\hat k\)  and  \(\vec b=2\hat i+4\hat j-9\hat k\)  find a unit vector parallel to  \(\vec a+\vec b.\)

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Best answer

Given that

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  \(\vec d=\vec a+\vec b\)

Then,

Both  \(\hat d\) and  \(-\vec d\) will be parallel to \(\hat d\), therefore the answer is 

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