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Let \alpha \epsilon R and the three vectors

\vec{a}=\alpha\hat{i}+\hat{j}+3\hat{k} , \vec{a}=2\hat{i}+\hat{j}-\alpha \hat{k} and 

\vec{a}=\alpha \hat{i}-2\hat{j}+3 \hat{k} . Then the set 

S=\left \{{\alpha: \vec{a},\vec{b}\: \: and \: \: \vec{c}\: \: are\: \: coplanar }}{ \right \}

  • Option 1)

    is singleton

  • Option 2)

    is empty

  • Option 3)

    contains exactly two positive numbers

  • Option 4)

    contains exactly two numbers only one of which is positive

 

Answers (1)

\begin{vmatrix} \alpha & 1 & 3\\ 2 & 1 & -4\\ \alpha & -2 &-3 \end{vmatrix}=0

=>  3\alpha ^{2}+18=0

=>  \alpha \epsilon \phi


Option 1)

is singleton

Option 2)

is empty

Option 3)

contains exactly two positive numbers

Option 4)

contains exactly two numbers only one of which is positive

Posted by

Vakul

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