Question

$A=\left[\begin{array}{ccc}{l}_1& m_1& n_1\\ l_2& m_2& n_2\\ l_3& m_3& n_3\end{array}\right]$ and $B=\left[\begin{array}{ccc}{p}_1& q_1& r_1\\ p_2& q_2& r_2\\ p_3& q_3& r_3\end{array}\right]$ where $p_1,q_1,r_1$ are the co-factors of the elements $l_i,m_i,n_i$ for $i=1,2,3$. If $(l_1,m_1,n_1),(l_2,m_2,n_2)$ and $(l_3,m_3,n_3)$ are the direction cosines of three mutually perpendicular lines then $(p_1,q_1,r_1),(p_2,q_2,r_2)$ and $(p_3,q_3,r_3)$ are

• A. The direction cosines of three mutually perpendicular lines
• B. The direction ratios of three mutually perpendicular lines which are not direction cosines
• C. The direction cosines of three lines which need not be perpendicular
• D. The direction ratios but not the direction cosines of three lines which need not be perpendicular

Answer 1

The correct option is A The direction cosines of three mutually perpendicular lines

Given $p_1,q_1,r_1$ are the co-factors of the elements $l_i,m_i,n_i$

For $i=1,2,3$

$(l_2,m_2,n_2)$ and $(l_3,m_3,n_3)$ are the direction cosines of three mutually perpendicular lines

Thus $(p_1,q_1,r_1),(p_2,q_2,r_2),(p_3,q_3,r_3)$ are also the direction cosines of three mutually perpendicular lines

Option A is Correct answer