A) \[\frac{x}{1}=\frac{y}{-3}=\frac{z}{5}\]
B) \[\frac{x}{-1}=\frac{y}{3}=\frac{z}{5}\]
C) \[\frac{x}{1}=\frac{y}{3}=\frac{z}{-5}\]
D) \[\frac{x}{1}=\frac{y}{4}=\frac{z}{-5}\]
Correct Answer: A
Solution :
[a] Let the line be \[\frac{x}{a}=\frac{y}{b}=\frac{z}{c}\] (i) If line (i) intersects with the line \[\frac{x-1}{2}\] \[=\frac{y+3}{4}=\frac{z-5}{3},\] Then \[\left| \begin{matrix} a & b & c \\ 2 & 4 & 3 \\ 4 & -3 & 14 \\ \end{matrix} \right|=0\Rightarrow 9a-7b-10c=0\] (ii) From (i) and (ii), we have \[\frac{a}{1}=\frac{b}{-3}=\frac{c}{5}\] \[\therefore \] The line is \[\frac{x}{1}=\frac{y}{-3}=\frac{z}{5}\]
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