Question:
The scalar product of the vector \(\vec{a}=\hat{i}-\hat{j}+2\hat{k}\) with a unit vector along sum of vectors \(\vec{b}=2\hat{i}-4\hat{j}+5\hat{k}\) and \(\vec{c}=\lambda\hat{i}-2\hat{j}-3\hat{k}\) is equal to 1. Find the value of \(\lambda\).