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Q5 Find \lambda and \mu  if ( 2 \hat i + 6 \hat j + 27 \hat k ) \times ( \hat i + \lambda j + \mu \hat k ) = \vec 0

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Given in the question

( 2 \hat i + 6 \hat j + 27 \hat k ) \times ( \hat i + \lambda j + \mu \hat k ) = \vec 0

and we need to find values of \lambda and \mu

\begin{vmatrix} \hat i &\hat j & \hat k\\ 2& 6&27 \\ 1& \lambda &\mu \end{vmatrix}=0

\hat i (6\mu-27\lambda)-\hat j(2\mu-27)+\hat k(2\lambda-6)=0

From Here we get,

6\mu-27\lambda=0

2\mu-27=0

2\lambda -6=0

From here, the value of  \lambda and \mu is

\lambda = 3 , \: and \: \mu=\frac{27}{2}

Posted by

Pankaj Sanodiya

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