The scalar product of the vector

    \[\widehat{i}+\widehat{j}+\widehat{k}\]

with a unit vector along the sum of vectors

    \[2\widehat{i}+4\widehat{j}-5\widehat{k}\]

and

    \[\lambda \widehat{i}+2\widehat{j}+3\widehat{k}\]

is equal to one. Find the value of

    \[\lambda \]

.