Vector Algebra

The scalar product of the vector \(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}\) with a unit vector along the sum of the vectors \(2 \hat{i}+4 \hat{j}-5 \hat{k}\) and \(\lambda \hat{i}+2 \hat{j}+3 \hat{k}\) is equal to 1 , then value of \(\lambda\) is