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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 R3, we get
0(−3+1)−λ(−1−2)+3(−1−6)=0
⇒3λ=21
⇒λ=7
Thus, the value of λ is 7.
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