Match List-I with List-II
| List-I | List-II | ||
| Equation of line | Point on the line, direction ratios of the line | ||
| (A) | \( \displaystyle\frac{x-5}{3}=\frac{y-2}{2}=\frac{z+4}{-8} \) | (I) | (−3, −2, 8), <5, 2, −4> |
| (B) | \( \displaystyle\frac{x+5}{3}=\frac{y+2}{2}=\frac{z-4}{-8} \) | (II) | (3, 2, −8), <5, 2, −4> |
| (C) | \( \displaystyle\frac{x-3}{5}=\frac{y-2}{2}=\frac{z+8}{-4} \) | (III) | (−5, −2, 4), <3, 2, −8> |
| (D) | \( \displaystyle\frac{x+3}{5}=\frac{y+2}{2}=\frac{z-8}{-4} \) | (IV) | (5, 2, −4), <3, 2, −8> |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) - (IV), (B) - (III), (C) - (II), (D) - (I)
The line \( \frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c} \) passes through \( (x_1,y_1,z_1) \) and has direction ratios <a, b, c>. The point is read with the signs reversed: x + 5 means \( x_1=-5 \).
(A) \( \frac{x-5}{3}=\frac{y-2}{2}=\frac{z+4}{-8} \)
This matches (IV) (5, 2, −4), <3, 2, −8>.
(B) \( \frac{x+5}{3}=\frac{y+2}{2}=\frac{z-4}{-8} \)
This matches (III) (−5, −2, 4), <3, 2, −8>.
(C) \( \frac{x-3}{5}=\frac{y-2}{2}=\frac{z+8}{-4} \)
This matches (II) (3, 2, −8), <5, 2, −4>.
(D) \( \frac{x+3}{5}=\frac{y+2}{2}=\frac{z-8}{-4} \)
This matches (I) (−3, −2, 8), <5, 2, −4>.
So the matching is (A)-(IV), (B)-(III), (C)-(II), (D)-(I).