Question

Find λ, if the vectors `veca=hati+3hatj+hatk,vecb=2hati−hatj−hatk and vecc=λhatj+3hatk`  are coplanar.

Answer 1

Since the vectors `veca=hati+3hatj+hatk,vecb=2hati−hatj−hatk and vecc=λhatj+3hatk` are coplanar.

`[veca vecb vecc]=0`

`=>|[1,3,1],[2,-1,-1],[0,lambda,3]|=0`

Expanding along R₃, we get

0(−3+1)−λ(−1−2)+3(−1−6)=0

⇒3λ=21

⇒λ=7

Thus, the value of λ is 7.