Three Dimensional Geometry Question 256
Question: The line $ \frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k} $ and $ \frac{x-1}{k}= $ $ \frac{y-4}{2}=\frac{z-5}{1} $ are coplanar, if
[AIEEE 2003]
Options:
A) $ k=0 $ or ?1
B) $ k=0 $ or 1
C) $ k=0 $ or ?3
D) $ k=3 $ or ?3
Show Answer
Answer:
Correct Answer: C
Solution:
$ | ,\begin{matrix} x_2-x_1 & y_2-y_1 & z_2-z_1 \\ l_1 & m_1 & n_1 \\ l_2 & m_2 & n_2 \\ \end{matrix}, |=0 $ $ \begin{vmatrix} 1 & -1 & -1 \\ 1 & 1 & -k \\ k & 2 & 1 \\ \end{vmatrix} =0\Rightarrow \begin{vmatrix} 0 & 0 & -1 \\ 2 & 1+k & -k \\ k+2 & 1 & 1 \\ \end{vmatrix} ,=,0 $ $ k^{2}+3k^{2}=0\Rightarrow k(k+3)=0 $ Þ $ k=0,\text{or }-3 $ .
BETA
