Find the value of `lambda` so that the following vectors are coplanar: ` vec a= hat i- hat j+ hat k , vec b=2 hat i+ hat j- hat k , vec c=lambda hat i- hat j+lambda hat k`

Explanation

Three vectors are coplanar when their scalar triple product is `0.`

`=> [veca vecb vecc] = 0`

`=>|[1,-1,1],[2,1,-1],[lambda,-1,lambda]| = 0`

`=>[1(lambda-1)+1(3lambda)+1(-2lambda -1)] = 0`

`=>lambda-1+3lambda-2lambda-1 = 0`

`=> 2lambda = 2`

`=>lambda = 1`, for which these three vectors will be coplanar.