Maharashtra State BoardHSC Arts 12th Board Exam
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Find λ, if the vectors a=i+3j+k,b=2i−j−k and c=λj+3k are coplanar. - Mathematics and Statistics

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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 R3, we get

0(3+1)λ(12)+3(16)=0

3λ=21

λ=7

Thus, the value of λ is 7.

Concept: Scalar Triple Product of Vectors
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