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If \(\vec A=\hat i+\hat j\) and \(\vec B=2\hat i+3\hat j\), then the unit vector along \(\vec A+\vec B\) is:

1. \(\hat i\) and \(\hat j\)
2. \(\frac{3\hat i+4\hat j}{5}\)
3. \(\frac{3\hat i+4\hat j}{5}\)
4. \(\frac{3\hat i-4\hat j}{5}\)

Correct answer: \(\frac{3\hat i+4\hat j}{5}\)

Solution

\(\vec A+\vec B=(1+2)\hat i+(1+3)\hat j=3\hat i+4\hat j\). Its magnitude is \(\sqrt{3^2+4^2}=5\), so the unit vector is \((3\hat i+4\hat j)/5\).

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