Vector Algebra: JEE Main 2021 Mathematics question

If the projection of the vector $\widehat i + 2\widehat j + \widehat k$ on the sum of the two vectors $2\widehat i + 4\widehat j - 5\widehat k$ and $- \lambda \widehat i + 2\widehat j + 3\widehat k$ is 1, then $\lambda$ is equal to __________.