If the lines $\frac{1-x}{3}=\frac{2 y-4}{4 K}=\frac{z-3}{2}$ and $\frac{x-1}{3 K}=\frac{1-y}{-1}=\frac{6-z}{5}$ are perpendicular, then the value of K is:

$-\frac{10}{7}$

The correct answer is Option (4) → $-\frac{10}{7}$

lines are perpendicular

$⇒(-3\hat i+\frac{4K}{2}\hat j+2\hat k).(3K\hat i+\hat j-5\hat k)=0$

$⇒-9K+2K-10=0$

$7K=-10$

$K=-\frac{10}{7}$