Find a vector of magnitude 5 units, and parallel to the resultant of the vectors $\overrightarrow a = 2\hat i + 3\hat j - \hat k$ and $\overrightarrow b = \hat i - 2\hat j + \hat k$ .

The resultant of given vectors $= \overrightarrow a + \overrightarrow b$

$= (2\hat i + 3\widehat j - \hat k) + (\hat i - 2\hat j + \hat k) = 3\hat i + \widehat j$

$\therefore$

Required vector of magnitude 5 units
$= 5\left( {\cfrac{{3\hat i + \hat j}}{{\sqrt {9 + 1} }}} \right) = \cfrac{3}{2}\sqrt {10} \hat i + \cfrac{{\sqrt {10} }}{2}\hat j$