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The number of distinct real values of β, for which the vectors -β 2 i + j + k , i - β 2 j + k and i + j - β 2 k are coplanar, is :- 0 1 2 3

The number of distinct real values of β, for which the vectors 


-β2i + j + k , i - β2 j + k and i + j - β2 k are coplanar, is :-



  1. 0

  2. 1

  3. 2

  4. 3

Grade:

1 Answers

Askiitians Expert Soumyajit IIT-Kharagpur
28 Points
14 years ago

Dear Rohit Rastogi,

Ans:- CORRECT ANS IS 2 

Let the vectors are a,b,c

As they are coplanar and hence [abc]=0

Solving we get an equation of β which is satisfied by real values of β , iff β²=2

Hence β=+√2 or -√2

Hence 2 values of β are possible.

 

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Regards,

Askiitians Experts
Soumyajit Das IIT Kharagpur

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