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If  \vec{a},\vec{b},\vec{c} are non-­coplanar vectors and \lambda is a real number, then the vectors \vec{a}+2\vec{b}+3\vec{c},\; \lambda\vec{b}+4\vec{c}\; \; and\; \; (2\lambda -1)\vec{c} are non-­coplanar for

  • Option 1)

    all except two values of \lambda

  • Option 2)

    all except one values of \lambda

  • Option 3)

    all values of  \lambda

  • Option 4)

    no value of   \lambda

 

Answers (1)

best_answer

As we learnt in 

Coplanar vectors -

\left [ \vec{a}\;\vec{b}\;\vec{c} \right ]=0

- wherein

\vec{a}, \vec{b} and \vec{c} are three vectors.

 

 Condition for given three vectors to be

Coplanar is \begin{vmatrix} 1 & 2 &3 \\ 0& \lambda &4 \\ 0 & 0 & 2\lambda-1 \end{vmatrix}=0

\Rightarrow \lambda(2\lambda -1)=0

\Rightarrow \lambda =0, \lambda=\frac{1}{2}

They are non coplanar for all real \lambda except \lambda=0,\frac{1}{2}


Option 1)

all except two values of \lambda

Correct

Option 2)

all except one values of \lambda

Incorrect

Option 3)

all values of  \lambda

Incorrect

Option 4)

no value of   \lambda

Incorrect

Posted by

divya.saini

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