#### Question

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

#### Solution

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 R_{3}, we get

0(−3+1)−λ(−1−2)+3(−1−6)=0

⇒3λ=21

⇒λ=7

Thus, the value of λ is 7.

Is there an error in this question or solution?

Solution Find λ, if the vectors a=i+3j+k,b=2i−j−k and c=λj+3k are coplanar. Concept: Scalar Triple Product of Vectors.