Find the value of $\lambda$ such that the vectors $\overrightarrow {\rm{a}} = 2\widehat {\rm{i}} + \lambda \widehat {\rm{j}} + \widehat {\rm{k}}$ and $\overrightarrow {\rm{b}} = \widehat {\rm{i}} + 2\widehat {\rm{j}} + 3\widehat {\rm{k}}$ are orthogonal.

Since, two non-zero vectors $\overrightarrow {\rm{a}}$ and $\overrightarrow {\rm{b}}$ are orthogonal i.e.,

$\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} = 0$.

$\therefore (2\widehat {\rm{i}} + \lambda \widehat {\rm{j}} + \widehat {\rm{k}}) \cdot (\widehat {\rm{i}} + 2\widehat {\rm{j}} + 3\widehat {\rm{k}}) = 0$

$\Rightarrow$ $2 + 2\lambda + 3 = 0$
$\lambda = \frac{{ - 5}}{2}$