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# Find λ, if the vectors a=i+3j+k,b=2i−j−k and c=λj+3k are coplanar. - CBSE (Science) Class 12 - Mathematics

ConceptScalar Triple Product of Vectors

#### 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(12)+3(16)=0

3λ=21

λ=7

Thus, the value of λ is 7.

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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.
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