Equation of a line passing through (1, 2, -3) which is parallel to the line \( \displaystyle\frac{x+2}{3}=\displaystyle\frac{y-3}{-4}=\displaystyle\frac{z+5}{5} \) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{x-1}{3}=\displaystyle\frac{y-2}{-4}=\displaystyle\frac{z+3}{5} \)
A parallel line has the same direction ratios (3, −4, 5). Through the point (1, 2, −3), its equation is
\( \displaystyle \frac{x-1}{3}=\frac{y-2}{-4}=\frac{z+3}{5} \)
Why the other options are incorrect
Option (1) \( \displaystyle\frac{x+1}{3}=\displaystyle\frac{y+2}{-4}=\displaystyle\frac{z-3}{5} \) — Incorrect. The signs of the point are reversed; this line passes through (−1, −2, 3).
Option (3) \( \displaystyle\frac{x-3}{1}=\displaystyle\frac{y+4}{2}=\displaystyle\frac{z-5}{-3} \) — Incorrect. Its direction ratios are (1, 2, −3), not (3, −4, 5).
Option (4) \( \displaystyle\frac{x+3}{1}=\displaystyle\frac{y-4}{2}=\displaystyle\frac{z+5}{-3} \) — Incorrect. Its direction ratios are (1, 2, −3), not (3, −4, 5).