Question

The lines $\frac{x}{1}=\frac{y}{2}=\frac{z}{3}$ and $\frac{x-1}{-2}=\frac{y-2}{-4}=\frac{z-3}{-6}$ are

• A. Parallel
• B. Intersecting
• C. Skew
• D. Coincident

Answer 1

The correct option is A Parallel

Direction ratios of line

$\frac{x}{1}=\frac{y}{2}=\frac{z}{3}$

are

$a_1=1,b_1=2,c_1=3$

And

direction ratios of the line

$\frac{x-1}{-2}=\frac{y-2}{-4}=\frac{z-3}{-6}$

are

$a_2=-2,b_2=-4,c_2=-6$

Now,

$\frac{a_1}{a_2}=\frac{-1}{2}$

$\frac{b_1}{b_2}=\frac{2}{-4}=\frac{-1}{2}$

$\frac{c_1}{c_2}=\frac{3}{-6}=\frac{-1}{2}$

Since,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Therefore, given lines are parallel.