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Prove that the three lines drown from origin with direction cosines (l_1,m_1,n_1),(l_2,m_2,n_2),(l_3,m_3,n_3) are coplanar if [[l_1,m_1,n_1],[l_2,m_2,n_2],[l_3,m_3,n_3]]=0.

Answer»

SOLUTION :LET ` OVERSETTOA=l_1i+m_1j+n_1koversettobl_2i+m_2j+n_2koversettocl_3i+m_3j+n_3k` The LINES co-planar if `oversettoa.(oversettobxxoversettoc)=0iff|(l_1,m_1,n_1),(l_2,m_2,n_2),(l_3,m_3,n_3):|=0`


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