Findthe value of `lambda`sothat 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`

Findthe value of `lambda`sothat the following vectors are coplanar:` v

1.	Findthe value of `lambda`sothat 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`
Answer» 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.