Question

Equation of a line passing through $(1, 2, -3)$ and parallel to the line $\frac{x-2}{1}=\frac{y+1}{3}=\frac{z-1}{4}$ is

• A. $\frac{x-1}{1}=\frac{y+2}{3}=\frac{z+3}{4}$
• B. $\frac{x-2}{1}=\frac{y+1}{2}=\frac{z-1}{-3}$
• C. $\frac{x-1}{1}=\frac{y-3}{2}=\frac{z-4}{-3}$
• D. None of these

Answer 1

Answer: (A)

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

Answer 2

Since, the line is parallel to the line $\frac{x-2}{1}=\frac{y+1}{3}=\frac{z-1}{4}$ $\therefore D$.$r$.$'s$ of the required line are $< 1$, $3$, $4>$ Hence, equation of the line passing through $\left(1,2, -3\right)$ with $d$.$r$.$'s\, < 1$, $3$ , $4 >$ is $\frac{x-1}{1}=\frac{y-2}{3}=\frac{z+3}{4}$