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 :-

0

1

2

3

Question

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

Askiitians Expert Soumyajit IIT-Kharagpur · Answer

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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Soumyajit Das IIT Kharagpur

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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 :-

0

1

2

3

1 Answers

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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 :- 0 1 2 3

1 Answers

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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 :-

0

1

2

3