Vector Algebra

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 __________.