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

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#### 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.

Concept: Scalar Triple Product of Vectors

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