Vector Algebra

The number of distinct real values of \(\lambda\), for which the vectors \(- {\lambda ^2}\widehat i + \widehat j + \widehat k,\widehat i - {\lambda ^2}\widehat j + \widehat k\) and \(\widehat i + \widehat j - {\lambda ^2}\widehat k\) are coplanar, is :