Determinants Matrices Question 160
Question: If $ l_r^{2}+m_r^{2}+n_r^{2}=1; $ $ r=1,2,3 $ and $ {l _{r}}{l _{s}}+m _{r}m _{s}+n _{r}n _{s}=0; $ $ r\ne s, $ $ r=1,2,3; $ $ s=1,2,3, $ then the value of $ \begin{vmatrix} {l_1} & m_1 & n_1 \\ {l_2} & m_2 & n_2 \\ {l_3} & m_3 & n_3 \\ \end{vmatrix} $ is
Options:
A) $ 0 $
B) $ \pm 1 $
C) $ 2 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ D^{2}= \begin{vmatrix} l_1 & m_1 & n_1 \\ l_2 & m_2 & n_2 \\ l_3 & m_3 & n_3 \\ \end{vmatrix} \begin{vmatrix} l_1 & m_1 & n_1 \\ l_2 & m_2 & n_2 \\ l_3 & m_3 & n_3 \\ \end{vmatrix} $
$ = \begin{vmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{vmatrix}=1\Rightarrow D=\pm 1 $
BETA
