Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (A) | Equations of line through (5, −4, 6) with direction ratios 3, 7, 2 | (I) | \(\displaystyle\frac{x+3}{5}=\frac{y+7}{-4}=\frac{z+2}{6}\) |
| (B) | Equations of line through (3, 7, 2) with direction ratios 5, −4, 6 | (II) | \(\displaystyle\frac{x-3}{5}=\frac{y-7}{-4}=\frac{z-2}{6}\) |
| (C) | Equations of line through (−5, 4, −6) with direction ratios 3, 7, 2 | (III) | \(\displaystyle\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}\) |
| (D) | Equations of line through (−3, −7, −2) with direction ratios 5, −4, 6 | (IV) | \(\displaystyle\frac{x+5}{3}=\frac{y-4}{7}=\frac{z+6}{2}\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
The line through \((x_1, y_1, z_1)\) with direction ratios a, b, c has the cartesian equations
\( \displaystyle \frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c} \)
The point's coordinates appear with their signs reversed in the numerators.
(A) Equations of line through (5, −4, 6) with direction ratios 3, 7, 2
This matches (III):
\( \displaystyle \frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2} \)
(B) Equations of line through (3, 7, 2) with direction ratios 5, −4, 6
This matches (II):
\( \displaystyle \frac{x-3}{5}=\frac{y-7}{-4}=\frac{z-2}{6} \)
(C) Equations of line through (−5, 4, −6) with direction ratios 3, 7, 2
This matches (IV):
\( \displaystyle \frac{x+5}{3}=\frac{y-4}{7}=\frac{z+6}{2} \)
(D) Equations of line through (−3, −7, −2) with direction ratios 5, −4, 6
This matches (I):
\( \displaystyle \frac{x+3}{5}=\frac{y+7}{-4}=\frac{z+2}{6} \)
So the matching is (A)-(III), (B)-(II), (C)-(IV), (D)-(I).