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  4. The value of P so that the vectors 2i-j+k, i+2j-3k and 3i+pj+5k are coplanar should be

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Q. The value of P so that the vectors $ 2i-j+k, $ $ i+2j-3k $ and $ 3i+pj+5k $ are coplanar should be

JamiaJamia 2012

Solution:

For coplanarity $ \left| \begin{matrix} 2 & -1 & 1 \\ 1 & 2 & -3 \\ 2 & P & 5 \\ \end{matrix} \right|=0 $ $ 2(10+3P)+1(5+9)+1(P-6)=0 $ $ 20+6P+5+9+P-6=0 $ $ 7P+34-6=0 $ $ 7P+28=0 $ $ 7P=-28 $ $ P=-\frac{28}{7}=-4 $